Precision Software Appli…tions Silver Collection 1/Precision Software Applications Silver Collection Volume One (PSM) (1993).iso/windows/games/fractdoc.exe/FRACTINT.DOC

Text File | 1990-12-08 | 276KB | 5,735 lines

                     Fractint Version 15.0                      Page 1


  New Features in Version 15.0...............................3

  Introduction...............................................5

  1. Fractint Commands.......................................7
      Plotting Commands......................................7
      Color Cycling Commands................................10
      Palette Editing Commands..............................11
      Save/Restore/Print Commands...........................14
      "3D" Commands.........................................15
      Interrupting and Resuming.............................15
      View Window...........................................16
      More Zoom Box Commands................................17
      Hints.................................................19

  2. Fractal Types..........................................20
      The Mandelbrot Set (type=mandel)......................20
      Julia Sets (type=julia)...............................21
      Newton domains of attraction (type=newtbasin).........22
      Newton (type=newton)..................................23
      Complex Newton (type=complexnewton/complexbasin)......23
      Lambda Sets (type=lambda).............................24
      Mandellambda Sets (type=mandellambda).................24
      Plasma Clouds (type=plasma)...........................24
      Lambdafn (type=lambdafn)..............................25
      Mandelfn (type=mandelfn)..............................26
      Barnsley Mandelbrot/Julia Sets (barnsleym1/.../j3)....26
      Barnsley IFS Fractals (type=ifs, ifs3d)...............27
      Sierpinski Gasket (type=sierpinski)...................28
      Quartic Mandelbrot/Julia (type=mandel4/julia4)........28
      Distance Estimator (distest=nnn)......................29
      Pickover Mandelbrot/Julia Types.......................29
      Pickover Popcorn (type=popcorn/popcornjul)............29
      Peterson Variations (xxmarksxx types).................30
      Unity (type=unity)....................................30
      Scott Taylor / Lee Skinner Variations.................31
      Kam Torus (type=kamtorus, kamtorus3d).................31
      Bifurcation (type=bifxxx).............................31
      Lorenz Attractors (type=lorenz/lorenz3d)..............33
      Rossler Attractors (type=rossler3D)...................34
      Henon Attractors (type=henon).........................34
      Pickover Attractors (type=pickover)...................35
      Gingerbreadman (type=gingerbreadman)..................35
      Test (type=test)......................................35
      Formula (type=formula)................................36
      Julibrots (type=julibrot).............................37
      Diffusion Limited Aggregation (type=diffusion)........39
      Magnetic Fractals (type=magnet1m/.../magnet2j)........39
      L-Systems (type=lsystem)..............................41

  3. Doodads, Bells, and Whistles...........................43
      Distance Estimator Method.............................43
      Inversion.............................................43
      Decomposition.........................................44

                     Fractint Version 15.0                      Page 2

      Logarithmic Palettes..................................45
      Biomorphs.............................................45
      Starfields............................................46

  4. "3D" Images............................................47
      3D Mode Selection.....................................47
      Select Fill Type Screen...............................49
      Stereo 3D Viewing.....................................50
      Rectangular Coordinate Transformation.................51
      Color Parameters......................................52
      Light Source Parameters...............................52
      Spherical Projection..................................53
      3D Overlay Mode.......................................54
      Special Note for CGA or Hercules Users................54
      Making Terrains.......................................55
      Making 3D Slides......................................56

  5. Command-Line Parameters, Setting Defaults, Batch Mode..58
      General Parameters....................................58
      Video Parameters......................................63
      Printer Parameters....................................65
      3D Parameters.........................................66
      Setting Defaults (SSTOOLS.INI)........................67
      Batch Mode............................................68

  6. File Formats, Color Maps and All That..................70
      Fractint and .GIF Files...............................70
      Continuous Potential..................................71
      Palette Maps..........................................73

  7. Hardware Support.......................................74
      Notes on Video Modes, "Standard" and Otherwise........74
      FRACTINT.CFG (Customized Video Mode List).............77

  8. Common Problems........................................79

  9. Fractals and the PC....................................81
      A Little History......................................81
       Before Mandelbrot ...................................81
       Who Is This Guy, Anyway? ............................82
      A Little Code.........................................83
       Periodicity Logic ...................................83
       Limitations of Integer Math (And How We Cope) .......84
       The Fractint "Fractal Engine" Architecture ..........85

  Appendix A  Mathematics of the Fractal Types..............87
  Appendix B  Stone Soup With Pixels: The Authors...........92
  Appendix C  Revision History..............................97
  Appendix D  Bibliography.................................103
  Appendix E  Other Programs...............................104
  Appendix F  Version13 to Version 14 Type Mapping.........105

                     Fractint Version 15.0                      Page 3

 New Features in Version 15.0

  New user interface! Enjoy!
  Some key assignments have changed and some have been removed.  If you're
  familiar with a prior version of Fractint, a quick exploration of the
  new main menu will show what is different.

  New palette editing from Ethan Nagel.

  Reduced memory requirements - Fractint now uses overlays and will run on
  a 512K machine. The bad news is that the executable can no longer be
  compressed with LZEXE, and has bloated up to almost 400K!

  New <v>iew command: use to get small window for fast preview, or to
  setup an image which will eventually be rendered on hard copy with
  different aspect ratio

  L-System fractal type from Adrian Mariano

  Postscript printer support from Scott Taylor

  Better Tandy video support and faster CGA video from Joseph A Albrecht

  16 bit continuous potential files have changed considerably;  see the
  Continuous Potential section for details.  Continuous potential is now
  resumable.

  Mandelbrot calculation is faster again (thanks to Mike Gelvin) - double
  speed in 8086 32 bit case

  Compressed log palette and sqrt palette from Chuck Ebbert

  Calculation automatically resumes whenever current image is resumable
  and is not paused for a visible reason.

  Auto increment of savename changed to be more predictable

  New video modes:
    trident 1024x768x256 mode
    320x480x256 tweak mode (good for reduced 640x480 viewing)
    changed NEC GB-1, hopefully it works now

  Integer mandelbrot and julia now work with periodicitycheck

  Initial zoombox color auto-picked for better contrast (usually)

  New adapter=cga|ega|mcga|vga for systems having trouble with auto-detect

  New textsafe=no|yes for systems having trouble with garbled text mode

  <r> and <3> commands now present list of video modes to pick from; <r>
  can reduce a non-standard or unviewable image size.

  Diffusion fractal type is now resumable after interrupt/save

                     Fractint Version 15.0                      Page 4

  Exitmode=n parameter, sets video mode to n when exiting from fractint

  When savetime is used with 1 and 2 pass and solid guessing, saves are
  deferred till the beginning of a new row, so that no calculation time is
  lost.

  3d photographer's mode now allows the first image to be saved to disk

  textcolors=mono|12/34/56/... -- allows setting user interface colors

  Code (again!) compilable under TC++ (we think!)

  bug fixes:

    multiple restores (msc 6.0, fixed in 14.0r)

    repeating 3d loads problem; slow 3d loads of images with float=yes

    map= is now a real substitute for default colors

    starfield and julibrot no longer cause permanent color map replacement

    starfield parameters bug fix - if you couldn't get the starfield
    parameters to do anything interesting before, try again with this
    release

    Newton and newtbasin orbit display fixed

  .TIW files (from v9.3) are no longer supported as input to 3D
  transformations

                     Fractint Version 15.0                      Page 5

 Introduction

  FRACTINT plots and manipulates images of "objects" -- actually, sets of
  mathematical points -- that have fractal dimension. See chapter 9 for
  some historical and mathematical background on fractal geometry, a
  discipline named and popularized by mathematician Benoit Mandelbrot. For
  now, these sets of points have three important properties:

  1) They are generated by relatively simple calculations repeated over
  and over, feeding the results of each step back into the next --
  something computers can do very rapidly.

  2) They are, quite literally, infinitely complex: they reveal more and
  more detail without limit as you plot smaller and smaller areas.
  Fractint lets you "zoom in" by positioning a small box and hitting
  <Enter> to redraw the boxed area at full-screen size; its maximum linear
  "magnification" is over a trillionfold.

  3) They can be astonishingly beautiful, especially using PC color
  displays' ability to assign colors to selected points, and (with VGA
  displays or EGA in 640x350x16 mode) to "animate" the images by quickly
  shifting those color assignments.

  The name FRACTINT was chosen because the program generates many of its
  images using INTeger math, rather than the floating point calculations
  used by most such programs. That means that you don't need a math co-
  processor chip (aka floating point unit or FPU), although for a few
  fractal types where floating point math is faster, the program
  recognizes and automatically uses an 80x87 chip if it's present. It's
  even faster on systems using Intel's 80386 and 80486 microprocessors,
  where the integer math can be executed in their native 32-bit mode.

  Fractint works with many adapters and graphics modes from CGA to the
  1024x768, 256-color 8514/A mode. Even "larger" images, up to
  2048x2048x256, can be plotted to expanded memory, extended memory, or
  disk: this bypasses the screen and allows you to create images with
  higher resolution than your current display can handle, and to run in
  "background" under multi-tasking control programs such as DESQview and
  Windows 3.

  Fractint is an experiment in collaboration. Many volunteers have joined
  Bert Tyler, the program's first author, in improving successive
  versions. Through electronic mail messages, first on CompuServe's PICS
  forum and now on COMART, new versions are hacked out and debugged a
  little at a time. Fractint was born fast, and none of us has seen any
  other fractal plotter close to the present version for speed,
  versatility, and all-around wonderfulness. (If you have, tell us so we
  can steal somebody else's ideas instead of each other's.) See Appendix B
  for information about the authors and how to contribute your own ideas
  and code.

                     Fractint Version 15.0                      Page 6

  Fractint is freeware. The copyright is retained by the Stone Soup Group.

  Conditions on use: Fractint may be freely copied and distributed but may
  not be sold. It may be used personally or in a business - if you can do
  your job better by using Fractint, or use images from it, that's great!
  It may be given away with commercial products under the following
  conditions:
   o It must be clearly stated that Fractint does not belong to the
     vendor and is included as a free give-away.
   o It must be a complete unmodified release of Fractint, with
     documentation, unless other arrangements are made with the Stone
     Soup Group

  There is no warranty of Fractint's suitability for any purpose, nor any
  acceptance of liability, express or implied.

  Source code for Fractint is also freely available. See the FRACTSRC.DOC
  file included with it for conditions on use. (In most cases we just want
  credit.)

  **********************************************************************
  * Contribution policy: Don't want money. Got money. Want admiration. *
  **********************************************************************

                     Fractint Version 15.0                      Page 7

 1. Fractint Commands

  To start the program, enter FRACTINT at the DOS prompt. The program
  displays an initial "credits" screen. Hitting <ENTER> gets you to the
  main menu. You can either select options from the menu by moving the
  highlight with the cursor, or you can enter commands directly.

  As soon as you select a video mode, the program begins drawing an
  initial display -- the "full" Mandelbrot set, if you haven't selected
  another fractal type.

  Help is available at any time by pressing the <F1> key.

  AT ANY TIME, you can hit one of the keys described in the following
  sections to select a function. You do not need to wait for a calculation
  to finish, nor do you have to return to the main menu.

  Note that for the "typewriter" keys, upper and lower case are
  equivalent, e.g. <B> and <b>, have the same result.

  Many commands and parameters can be passed to FRACTINT.EXE as command-
  line arguments or read from a configuration file; see Chapter 5 for
  details.


 Plotting Commands

  Function keys & various combinations are used to select a video mode and
  redraw the screen.  For a quick start, try one of the following:
    If you have MCGA, VGA, or better:  <F3>
    If you have EGA:                   <F9>
    If you have CGA:                   <F5>
    Otherwise, monochrome:             <F6>
  When you choose "select video mode" from the main menu, you will see a
  list of possible video modes.

  <F1>
  Display a help screen.  The function keys available in help mode are
  displayed at the bottom of the help screen.

  <M> or <Esc>
  Return from a displayed image to the main menu.

  <Esc>
  From the main menu, <Esc> is used to exit from Fractint.

  <Page Up>
  Display and shrink the zoom box ("zoom in"). The LEFT button of a mouse
  displays the box; push the mouse away from you while holding that button
  down to shrink the box.

  <Page Down>
  Display and expand the zoom box ("zoom out"). Pulling the mouse towards
  you with the left button down has the same effect.

                     Fractint Version 15.0                      Page 8

  Cursor ("arrow") keys
  Move ("pan") the zoom box. Moving the mouse has the same effect. With an
  enhanced-keyboard BIOS, <Ctrl> plus a cursor key moves the box 5 times
  faster.

  <Enter> ("Return")
  Redraw the area inside the zoom box as a full-screen image. Or double
  click the left mouse button.  If there's no zoom box on the screen, and
  the current image is incomplete (e.g. if you interrupted it to adjust
  the colors)
  Enter is also used to resume calculation after a pause. It is only
  necessary to do this when there is a message on the screen waiting to be
  acknowledged, such as the message shown after you save an image to disk.

  <Ctrl><Enter>
  "Zoom out," so that your screen would fill the current zoom box, and
  redraw.  Or double click the right mouse button.

  <\> (previously <HOME>)
  Redraw the previous image. The program tracks 25 sets of pervious
  coordinates and fractal types, but does not remember other options which
  were different for those past images.

  <Tab>
  Display the current fractal type, parameters, screen or (if displayed)
  zoom-box coordinates, maximum iteration count, and other information
  useful in keeping track of where you are.  The Tab function is non-
  destructive - if you press it while in the midst of generating an image,
  you will continue generating it when you return.  The Tab function tells
  you if your image is still being generated or has finished - a handy
  feature for those overnight, 1024x768 resolution fractal images.  If the
  image is incomplete, it also tells you whether it can be interrupted and
  resumed.  (Any function other than <Tab> and <F1> counts as an
  "interrupt".)

  <T>
  Select a fractal type. Move the cursor to your choice and hit <Enter>.
  Next you will be prompted for any parameters used by the selected type -
  hit Enter to use the defaults. Note that any values you change on this
  parameter screen are remembered for the next time you select the same
  type.

  <X>
  Select a number of eXtended options. Brings up a full-screen menu of
  options, any of which you can change at will.  These options are:
    Image generation algorithm ("passes=" option)
    Floating point algorithm toggle
    "maxiter=" iteration maximum
    "inside=" and "outside=" colors
    "logmap=" logarithmic palette value
    "biomorph=" option
    "decomp=" decomposition value
    "sound=" option
    "overwrite=" option
    "distest=" value

                     Fractint Version 15.0                      Page 9

    "savename=" filename
  The "passes option" (which used to be selected by <1>, <2>, or <G>)
  selects single-pass, dual-pass, or solid-guessing (default) mode, then
  redraws the screen. Single-pass mode draws the screen pixel by pixel.
  Dual-pass generates a "coarse" screen first as a preview using 2x2-pixel
  boxes, and then generates the rest of the dots with a second pass.
  Solid-guessing performs from two to four visible passes - more passes in
  higher resolution video modes. Its first visible pass is actually two
  passes - one pixel per 4x4, 8x8, or 16x16 pixel box (depending on number
  of passes) is generated, and the guessing logic is applied to fill in
  the blocks at the next level (2x2, 4x4, or 8x8). Subsequent passes fill
  in the display at the next finer resolution, skipping blocks which are
  surrounded by the same color. Solid-guessing can guess wrong, but it
  sure guesses quickly! Note: these options, along with the Boundary-
  Tracing alternative, can now also be selected using the "X" options
  screen.  Boundary Tracing, which only works with fractal types (such as
  the Mandelbrot set, but not the Newton type) that do not contain
  "islands" of colors, finds a color "boundary", traces it around the
  screen, and then "blits" in the color over the enclosed area.
  Floating point is discussed below, under the <F> key.
  The other extended options are detailed elsewhere in the manual.

  <Y>
  More options which we couldn't fit under the <X> command. Finite
  attractor option, continuous potential parameters, and inversion
  options. These options are discussed elsewhere in the manual.

  <Spacebar>
  Toggle between Mandelbrot set images and their corresponding Julia-set
  images. Read the notes in chapter 2 before trying this option if you
  want to see anything interesting.

  <B>
  Create a batch file, FRABATCH.BAT, that will start Fractint with the
  command-line arguments needed to draw the current image. If FRABATCH.BAT
  already exists, a new line is appended to it.

  <F>
  Toggles the use of floating-point algorithms. Whether floating point is
  in use is shown on the <Tab> status screen.  The floating point option
  can also be turned on and off using the "X" options screen.

  <I>
  Call up an editor that modifies, saves and restores various parameters.
  Currently you can change the coefficients used in plotting the Barnsley
  IFS fractal types or the 3D transformations used with the "Lorenz3D" and
  "IFS3D" fractal types, including the selection of "funny glasses"
  red/blue 3D.

  <O> (the letter, not the number)
  If pressed while an image is being generated, toggle the display of
  intermediate results -- the "orbits" Fractint uses as it calculates
  values for each point. Slows the display a bit, but shows you how clever
  the program is being behind the scenes. (See "A Little Code" in chapter
  9.)

                     Fractint Version 15.0                     Page 10


  <Insert>
  Restart at the "credits" screen and reset most variables to their
  initial state.  Variables which are not reset are: savename, lightname,
  ifs parms, video, startup filename.

  <D>
  Shell to DOS. Return to Fractint by entering "exit" at a DOS prompt.


 Color Cycling Commands

  The color-cycling commands are available ONLY for VGA adapters and EGA
  adapters in 640x350x16 mode.

  Note that the palette colors available on an EGA adapter (16 colors at a
  time out of a palette of 64) are limited compared to those of VGA,
  super-VGA, and MCGA (16 or 256 colors at a time out of a palette of
  262,144). So color-cycling in general looks a LOT better in the latter
  modes. Also, because of the EGA palette restrictions, some commands are
  not available with EGA adapters.

  <+> or <->
  Switch to color-cycling mode and begin cycling the palette by shifting
  each color to the next "contour."

  <C>
  Switch to color-cycling mode but do not start cycling. The normally
  black "overscan" border of the screen changes to white.

  When you are in color-cycling mode, you will either see the screen
  colors cycling, or will see a white "overscan" border when paused, as a
  reminder that you are still in this mode.  The keyboard commands
  available once you've entered color-cycling. are described below.

  <F1>
  Bring up a HELP screen with commands specific to color cycling mode.

  <Esc>
  Leave color-cycling mode.

  <+> or cursor->, <-> or cursor<-
  Reverse the cycling direction "out" or "in."

  Cursor up/down
  Increase/decrease the cycling speed. High speeds may cause a harmless
  flicker at the top of the screen.

  <F2> through <F10>
  Switches from simple rotation to color selection using randomly
  generated color bands of short (F2) to long (F10) duration.

  <1> through <9>
  Causes the screen to be updated every 'n' color cycles (the default is
  1). Handy for slower computers.

                     Fractint Version 15.0                     Page 11


  <Enter>
  Randomly selects a function key (F2 through F10) and then updates ALL
  the screen colors prior to displaying them for instant, random colors.
  Hit this over and over again (we do).

  <Spacebar>
  Pause cycling with white overscan area. Cycling restarts with any
  command key (including another spacebar).

  <Shift><F1>-<F10>
  Pause cycling and reset the palette to a preset two color "straight"
  assignment, such as a spread from black to white. (Not for EGA)

  <Ctrl><F1>-<F10>
  Pause and use a two-color cyclical assignment, e.g. red->yellow->red
  (not for EGA).

  <Alt><F1>-<F10>
  Pause and use a 3-color cyclical assignment, e.g. green->white->blue
  (not for EGA).

  <R>, <G>, <B>
  Pause and increase the red, green, or blue component of all colors by a
  small amount (not for EGA). Note the case distinction of this vs:

  <r>, <g>, <b>
  Pause and decrease the red, green, or blue component of all colors by a
  small amount (not for EGA).

  <D> or <A>
  Pause and load an external color map from the files DEFAULT.MAP or
  ALTERN.MAP, supplied with the program.

  <L>
  Pause and load an external color map (.MAP file).  Several .MAP files
  are supplied with Fractint. (See chapter 6 for details on creating your
  own map files manually, or save customized palettes in .MAP files using
  the <S> command in color-cycling or palette-editing mode.)

  <S>
  Pause, prompt for a filename, and save the current palette to the named
  file (.MAP assumed).


 Palette Editing Commands

  Palette-editing mode provides a number of tools for modifying the colors
  in an image.  It can be used only with 256 color images.

  Use the <E> key to enter palette-editing mode from a displayed image or
  from the main menu.

  When this mode is entered, an empty palette frame is displayed. You can
  use the cursor keys to position the frame outline, and <Pageup> and

                     Fractint Version 15.0                     Page 12

  <Pagedn> to change its size.  (The upper and lower limits on the size
  depend on the current video mode.)  When the frame is positioned where
  you want it, hit Enter to display the current palette in the frame.

  Note that the palette frame shows R(ed) G(reen) and B(lue) values for
  two color registers at the top.  The active color register has a solid
  frame, the inactive register's frame is dotted.  Within the active
  register, the active color component is framed.

  Using the commands described below, you can assign particular colors to
  the registers and manipulate them.  Note that color zero (top left)
  cannot be edited.  Color 255 (bottom right) is also special - it can
  only be edited by rotating the palette to move it to another slot, then
  editing that slot and rotating the palette back again.

  Once the palette frame is displayed and filled in, the following
  commands are available:

  <F1>
  Bring up a HELP screen with commands specific to palette-editing mode.

  <Esc>
  Leave palette-editing mode

  <H>
  Hide the palette frame to see full image; the cross-hair remains visible
  and all functions remain enabled; hit <H> again to restore the palette
  display.

  Cursor keys
  Move the cross-hair cursor around. In 'auto' mode (the default) the
  color under the center of the cross-hair is automatically assigned to
  the active color register. Control-Cursor keys move the cross-hair
  faster. A mouse can also be used to move around.

  <R> <G> <B>
  Select the Red, Green, or Blue component of the active color register
  for subsequent commands

  <Insert> <Delete>
  Select previous or next color component in active register

  <+> <->
  Increase or decrease the active color component value by 1  Numeric
  keypad (gray) + and - keys do the same.

  <Pageup> <Pagedn>
  Increase or decrease the active color component value by 5; Moving the
  mouse up/down with left button held is the same

  <0> <1> <2> <3> <4> <5>
  Set the active color component's value to 0 10 20 ... 60

  <Space>
  Select the other color register as the active one.  In the default

                     Fractint Version 15.0                     Page 13

  'auto' mode this results in the now-inactive register being set to
  remember the color under the cursor, and the now-active register
  changing from whatever it had previously remembered to now follow the
  color.

  <,> <.>
  Rotate the palette one step.  The rotation matches the color-cycling
  mode rotation method - only colors 1 through 255 inclusive are involved.

  "<" ">"
  Rotate the palette continuously (until next keystroke)

  <C>
  Enter Color-Cycling Mode.  When you invoke color-cycling from here, it
  will subsequently return to palette-editing when you <Esc> from it.

  <=>
  Create a smoothly shaded range of colors between the colors selected by
  the two color registers.

  <D>
  Duplicate the inactive color register's values to the active color
  register.

  <T>
  Stripe-shade - create a smoothly shaded range of colors between the two
  color registers, setting only every Nth register.  After hitting <T>,
  hit a numeric key from 2 to 9 to specify N.  For example, if you press
  <T> <3>, smooth shading is done between the two color registers,
  affecting only every 3rd color between them.  The other colors between
  them remain unchanged.

  <Shift-F2> ... <Shift-F9>
  Store the current palette in a temporary save area associated with the
  function key.  The temporary save palettes are useful for quickly
  comparing different palettes or the effect of some changes - see next
  command.  The temporary palettes are only remembered until you exit from
  palette-editing mode.

  <F2> ... <F9>
  Restore the palette from a temporary save area.  If you haven't
  previously saved a palette for the function key, you'll get a simple
  grey scale.

  <\>
  Move or resize the palette frame.  The frame outline is drawn - it can
  then be repositioned and sized with the cursor keys, <Pageup> and
  <Pagedn>, just as was done when first entering palette-editing mode.
  Hit Enter when done moving/sizing

  <I>
  Invert frame colors.  With some colors the palette is easier to see when
  the frame colors are interchanged.

                     Fractint Version 15.0                     Page 14

  <L>
  Pause and load an external color map (.MAP file).

  <S>
  Pause, prompt for a filename, and save the current palette to the named
  file (.MAP assumed).

  <A>
  Toggle 'auto' mode on or off.  When on (the default), the active color
  register follows the cursor; when off, <Enter> must be pressed to set
  the active register to the color under the cursor.

  <Enter>
  Only useful when 'auto' is off, as described above; double clicking the
  left mouse button is the same as Enter

  <X>
  Toggle 'exclude' mode on or off - when toggled on, only those image
  pixels which match the active color are displayed.

  <Y>
  Toggle 'exclude' range on or off - similar to <X>, but all pixels
  matching colors in the range of the two color registers are displayed.


 Save/Restore/Print Commands

  <S>
  Save the screen contents to disk. Progress is marked by colored lines
  moving down the screen's edges. The default filename is FRACT001.GIF;
  multiple saves in a session are automatically incremented 002, 003...
  Use the "savename=" parameter or <X> options screen to change the name.
  By default, files left over from previous sessions are not overwritten -
  the first unused FRACTnnn name is used.  Use the "overwrite=yes"
  parameter or <X> options screen) to overwrite existing files.  A save
  operation can be interrupted by pressing any key. If you interrupt,
  you'll be asked whether to keep or discard the partial file.

  <R>
  Restore an image previously saved with <S>, or an ordinary GIF file.
  After pressing <R> you are shown the file names in the current directory
  which match the current file mask. To select a file to restore, move the
  cursor to it and press <Enter>.

  Directories are shown in the file list with a "\" at the end of the
  name. When you select a directory, the contents of that directory are
  shown. Or, you can type the name of a different directory (and
  optionally a different drive) and press <Enter> for a new display. You
  can also type a mask such as "*.XYZ" and press <Enter> to display files
  whose name ends with the matching suffix (XYZ).

  Once you have selected a file to restore, a summary description of the
  file is shown, with a video mode selection list. Usually you can just
  press <Enter> to go past this screen and load the image. Other choices
  available at this point are:

                     Fractint Version 15.0                     Page 15

    Cursor keys: select a different video mode
    <Tab>: display more information about the fractal
    <F1>: for help about the "err" column in displayed video modes
  If you restore a file into a video mode which does not have the same
  pixel dimensions as the file, Fractint will make some adjustments:  The
  view window parameters (see <V> command) will automatically be set to an
  appropriate size, and if the image is larger than the screen dimensions,
  it will be reduced by using only every Nth pixel during the restore.

  <P>
  Print the current fractal image on your (Laserjet, Paintjet, Epson-
  compatible, or PostScript) printer. See chapter 5 for how to let
  Fractint know about your printer setup. "Disk video" modes can be used
  to generate images for printing at higher resolutions than your screen
  supports.


 "3D" Commands

  <3>
  Restore a saved image as a 3D "landscape", translating its color
  information into "height". You will be prompted for all KINDS of
  options;  see the "3D Images" chapter for details.

  <O>
  Restore in 3D and overlay the result on the current screen. (This only
  works when there's a completed image on screen, so it can't be confused
  with the <O>-for-orbits toggle that ONLY operates WHILE a fractal is
  being generated.)


 Interrupting and Resuming

  Fractint command keys can be loosely grouped as:

   o Keys which suspend calculation of the current image (if one is being
     calculated) and automatically resume after the function.  <Tab>
     (display status information) and <F1> (display help), are the only
     keys in this group.

   o Keys which automatically trigger calculation of a new image.
     Examples:  selecting a video mode (e.g. <F3>);  selecting a fractal
     type using <T>;  using the <X> screen to change an option such as
     maximum iterations.

   o Keys which do something, then wait for you to indicate what to do
     next.  Examples:  <M> to go to main menu;  <C> to enter color
     cycling mode;  <PageUp> to bring up a zoom box.  After using a
     command in this group, calculation automatically resumes when you
     return from the function (e.g. <Esc> from color cycling, <PageDn> to
     clear zoom box).  There are a few fractal types which cannot resume
     calculation, they are noted below.  Note that after saving an image
     with <S>, you must press <Enter> to clear the "saved" message from
     the screen and resume.

                     Fractint Version 15.0                     Page 16

  An image which is <S>aved before it completes can later be <R>estored
  and continued. The calculation is automatically resumed when you restore
  such an image.

  When a slow fractal type resumes after an interruption in the third
  category above, there may be a lag while nothing visible happens.  This
  is because most cases of resume restart at the beginning of a screen
  line.  If unsure, you can check whether calculation has resumed with the
  <Tab> key.

  The following fractal types cannot (currently) be resumed: plasma, 3d
  transformations, julibrot, and 3d orbital types like lorenz3d.  To check
  whether resuming an image is possible, use the <Tab> key while it is
  calculating.  It is resumable unless there is a note under the fractal
  type saying it is not.

  The "Batch Mode" section discusses how to resume in batch mode.

  To <R>estore and resume a "formula" type fractal (described later) your
  "formulafile" must contain the required formula.


 View Window

  The <V> command is used to set the view window parameters described
  below. These parameters can be used to:
   o Define a small window on the screen which is to contain the
     generated images. Using a small window speeds up calculation time
     (there are less pixels to generate). You can use a small window to
     explore quickly, then turn the view window off to recalculate the
     image at full screen size.
   o Generate an image with a different "aspect ratio"; e.g. in a square
     window or in a tall skinny rectangle.
   o View saved GIF images which have pixel dimensions different from any
     mode supported by your hardware. This use of view windows occurs
     automatically when you restore such an image.

  Note that there are currently no command-line parameters for view
  windows - they can only be set interactively.

  "Preview display"
  Set this to "yes" to turn on view window, "no" for full screen display.
  While this is "no", the only view parameter which has any affect is
  "final media aspect ratio". When a view window is being used, all other
  Fractint functions continue to operate normally - you can zoom, color-
  cycle, and all the rest.

  "Reduction factor"
  When an explicit size is not given, this determines the view window
  size, as a factor of the screen size.  E.g. a reduction factor of 2
  makes the window 1/2 as big as the screen in both dimensions.

  "Final media aspect ratio"
  This is the height of the final image you want, divided by the width.
  The default is 0.75 because standard PC monitors have a height:width

                     Fractint Version 15.0                     Page 17

  ratio of 3:4. E.g. set this to 2.0 for an image twice as high as it is
  wide. The effect of this parameter is visible only when "preview
  display" is enabled.

  "Crop starting coordinates"
  This parameter affects what happens when you change the aspect ratio. If
  set to "no", then when you change aspect ratio, the prior image will be
  squeezed or stretched to fit into the new shape. If set to "yes", the
  prior image is "cropped" to avoid squeezing or stretching.

  "Explicit size"
  Setting these to non-zero values over-rides the "reduction factor" with
  explicit sizes in pixels. If only the "x pixels" size is specified, the
  "y pixels" size is calculated automatically based on x and the aspect
  ratio.

  More about final aspect ratio:  If you want to produce a high quality
  hard-copy image which is say 8" high by 5" down, based on a vertical
  "slice" of an existing image, you could use a procedure like the
  following. You'll need some method of converting a GIF image to your
  final media (slide or whatever) - Fractint can only do the whole job
  with a PostScript printer, it does not preserve aspect ratio with other
  printers.
   o restore the existing image
   o set view parameters: preview to yes, reduction to anything (say 2),
     aspect ratio to 1.6, and crop to yes
   o zoom, rotate, whatever, till you get the desired final image
   o set preview display back to no
   o trigger final calculation in some high res disk video mode, using
     the appropriate video mode function key
   o print directly to a PostScript printer, or save the result as a GIF
     file and use external utilities to convert to hard copy.


 More Zoom Box Commands

  In addition to resizing the zoom box and moving it around, you can do
  some rather warped things with it. The general approach is always the
  same:  Frame an area, then <Enter> to expand what's in the frame to fill
  the whole screen (zoom in); or <Ctrl><Enter> to shrink the current image
  into the framed area (zoom out). With a mouse, double-click the left
  button to zoom in, double click the right button to zoom out.

  <Page Up>, <Page Down>
  Use <Page Up> to initially bring up the zoom box. It starts at full
  screen size. Subsequent use of these keys makes the zoom box smaller or
  larger. Using <Page Down> to enlarge the zoom box when it is already at
  maximum size removes the zoom box from the display. Moving the mouse
  away from you or toward you while holding the left button down performs
  the same functions as these keys.

  The cursor "arrow" keys, holding <Ctrl> with the "arrow" keys, and
  moving the mouse without holding any buttons down, moves the zoom box.

                     Fractint Version 15.0                     Page 18

  Panning: If you move a fullsize zoombox and don't change anything else
  before performing the zoom, Fractint just moves what's already on the
  screen and then fills in the new edges, to reduce drawing time. This
  feature applies to most fractal types but not all.  A side effect is
  that while an image is incomplete, a full size zoom box moves in steps
  larger than one pixel.  Fractint keeps the box on multiple pixel
  boundaries, to make panning possible.  As a multi-pass (e.g. solid
  guessing) image approaches completion, the zoom box can move in smaller
  increments.

  <Ctrl><Keypad->, <Ctrl><Keypad+>
  Holding <Ctrl> and pressing the numeric keypad's + or - keys rotates the
  zoom box. Moving the mouse left or right while holding the right button
  down performs the same function.

  <Ctrl><Page Up>, <Ctrl><Page Down>
  These commands change the zoom box's "aspect ratio", stretching or
  shrinking it vertically. Moving the mouse away from you or toward you
  while holding both buttons (or the middle button on a 3-button mouse)
  down performs the same function. There are no commands to directly
  stretch or shrink the zoom box horizontally - the same effect can be
  achieved by combining vertical stretching and resizing.

  <Ctrl><Home>, <Ctrl><End>
  These commands "skew" the zoom box, moving the top and bottom edges in
  opposite directions. Moving the mouse left or right while holding both
  buttons (or the middle button on a 3-button mouse) down performs the
  same function. There are no commands to directly skew the left and right
  edges - the same effect can be achieved by using these functions
  combined with rotation.

  <Ctrl><Insert>, <Ctrl><Delete>
  These commands change the zoom box color. This is useful when you're
  having trouble seeing the zoom box against the colors around it. Moving
  the mouse away from you or toward you while holding the right button
  down performs the same function.

  You may find it difficult to figure out what combination of size,
  position, rotation, stretch, and skew to use to get a particular result.
  (We do.) A good way to get a feel for all these functions is to play
  with the Gingerbreadman fractal type. Gingerbreadman's shape makes it
  easy to see what you're doing to him. A warning though: Gingerbreadman
  will run forever, he's never quite done! So, pre-empt with your next
  zoom when he's baked enough.

  If you accidentally change the shape of your zoom box, or rotate and
  forget which way is up, just use <Page Down> to make it bigger until it
  is removed from the display, then <Page Up> to get a fresh one. With the
  mouse, after removing the old zoom box from the display, release and re-
  press the left button to get a fresh one.

  If your screen does not have a 4:3 "aspect ratio" (i.e. if the visible
  display area on it is not 1.333 times as wide as it is high), rotating
  and zooming will have some odd effects - angles will change, including
  the zoom box's shape itself, circles (if you are so lucky as to see any

                     Fractint Version 15.0                     Page 19

  with a non-standard aspect ratio) become non-circular, and so on. The
  vast majority of PC screens *do* have a 4:3 aspect ratio.

  Zooming is not implemented for the plasma and diffusion fractal types,
  nor for <O>verlayed and <3>d images. A few fractal types support zooming
  but do not support rotation and skewing - nothing happens when you try
  it.


 Hints

  Remember, you do NOT have to wait for the program to finish a full
  screen display before entering a command. If you see an interesting spot
  you want to zoom in on while the screen is half-done, don't wait -- do
  it! If you think after seeing the first few lines that another video
  mode would look better, go ahead -- Fractint will shift modes and start
  the re-draw at once. When it finishes a display, it beeps and waits for
  your next command.

  In general, the most interesting areas are the "border" areas where the
  colors are changing rapidly. Zoom in on them for the best results. The
  first Mandelbrot-set (default) fractal image has a large, solid-colored
  interior that is the slowest to display; there's nothing to be seen by
  zooming there.

  Plotting time is directly proportional to the number of pixels in a
  screen, and hence increases with the resolution of the video mode. After
  you get used to the first "zoom levels," you may want to start in a low-
  resolution mode for quick progress, and switch to a higher-resolution
  mode when things get interesting. Or use the <G>uessing mode and pre-
  empt with a zoom before it finishes. Plotting time also varies with the
  maximum iteration setting, the fractal type, and your choice of drawing
  mode. Solid-guessing (the default) is fastest, but it can be wrong:
  perfectionists will want to use dual-pass mode (its first-pass preview
  is handy if you might zoom pre-emptively) or single-pass mode.

  When you start systematically exploring, you can save time (and hey,
  every little bit helps -- these "objects" are INFINITE, remember!) by
  <S>aving your last screen in a session to a file, and then going
  straight to it the next time with FRACTINT FRACTxxx (the .GIF extension
  is assumed). Or you could simply hit <B> to create a batch file with the
  "recipe" for a given image, and next time start with FRABATCH to re-plot
  it. See chapter 6 for more on batch mode and the command-line arguments
  the <B> command writes.

                     Fractint Version 15.0                     Page 20

 2. Fractal Types


  This section is intended only as a quick introduction to the types; more
  detail on the mathematics of types other than the Mandelbrot set can be
  found in Appendix A, and some notes on how Fractint calculates them in
  chapter 9.

  Fractint starts by default with the Mandelbrot set. You can change that
  by firing it up with the command-line argument "TYPE=" followed by one
  of the names in parentheses below, or within the program by hitting <T>
  and typing in the name. If parameters are needed, you will be prompted
  for them.

  In the text that follows, due to the limitations of the ASCII character
  set, "a*b" means "a times b", and "a^b" means "a to the power b".


 The Mandelbrot Set (type=mandel)

  This set is the classic: the only one implemented in many plotting
  programs, and the source of most of the printed fractal images published
  in recent years. Like most of the other types in Fractint, it is simply
  a graph: the x (horizontal) and y (vertical) coordinate axes represent
  ranges of two independent quantities, with various colors used to
  symbolize levels of a third quantity which depends on the first two. So
  far, so good: basic analytic geometry.

  Now things get a bit hairier. The x axis is ordinary, vanilla real
  numbers. The y axis is an imaginary number, i.e. a real number times i,
  where i is the square root of -1. Every point on the plane -- in this
  case, your PC's display screen -- represents a complex number of the
  form:

  x-coordinate + i * y-coordinate

  If your math training stopped before you got to imaginary and complex
  numbers, this is not the place to catch up. Suffice it to say that they
  are just as "real" as the numbers you count fingers with (they're used
  every day by electrical engineers) and they can undergo the same kinds
  of algebraic operations.

  OK, now pick any complex number -- any point on the complex plane -- and
  call it C, a constant. Pick another, this time one which can vary, and
  call it Z. Starting with Z=0 (i.e., at the origin, where the real and
  imaginary axes cross), calculate the value of the expression

  Z^2 + C

  Take the result, make it the new value of the variable Z, and calculate
  again. Take that result, make it Z, and do it again, and so on: in
  mathematical terms, iterate the function Z(n+1) = Z(n)^2 + C. For
  certain values of C, the result "levels off" after a while. For all
  others, it grows without limit. The Mandelbrot set you see at the start
  -- the solid-colored lake (blue by default), the blue circles sprouting

                     Fractint Version 15.0                     Page 21

  from it, and indeed every point of that color -- is the set of all
  points C for which the value of Z is less than 2 after 150 iterations
  (default setting). All the surrounding "contours" of other colors
  represent points for which Z exceeds 2 after 149 iterations (the contour
  closest to the M-set itself), 148 iterations, (the next one out), and so
  on.

  Some features of interest:

  1. Use the <X> options screen to increase the number of iterations.
  Notice that the boundary of the M-set becomes more and more convoluted
  (the technical terms are "wiggly," "squiggly," and "utterly bizarre") as
  the Z-values for points that were still within the set after 150
  iterations turn out to exceed 2 after 200, 500, or 1200. In fact, it can
  be proven that the true boundary is infinitely long: detail without
  limit.

  2. Although there appear to be isolated "islands" of blue, zoom in --
  that is, plot for a smaller range of coordinates to show more detail --
  and you'll see that there are fine "causeways" of blue connecting them
  to the main set. As you zoomed, smaller islands became visible; the same
  is true for them. In fact, there are no isolated points in the M-set: it
  is "connected" in a strict mathematical sense.

  3. The upper and lower halves of the first image are symmetric (a fact
  that Fractint makes use of here and in some other fractal types to speed
  plotting). But notice that the same general features -- lobed discs,
  spirals, starbursts -- tend to repeat themselves (although never
  exactly) at smaller and smaller scales, so that it can be impossible to
  judge by eye the scale of a given image.

  4. In a sense, the contour colors are window-dressing: mathematically,
  it is the properties of the M-set itself that are interesting, and no
  information about it would be lost if all points outside the set were
  assigned the same color. If you're a serious, no-nonsense type, you may
  want to cycle the colors just once to see the kind of silliness that
  other people enjoy, and then never do it again. Go ahead. Just once,
  now. We trust you.


 Julia Sets (type=julia)

  These sets were named for mathematician Gaston Julia, and can be
  generated by a simple change in the iteration process described above.
  Start with a specified value of C, "C-real + i * C-imaginary"; use as
  the initial value of Z "x-coordinate + i * y-coordinate"; and repeat the
  same iteration, Z(n+1) = Z(n)^2 + C.

  There is a Julia set corresponding to every point on the complex plane -
  - an infinite number of Julia sets. But the most visually interesting
  tend to be found for the same C values where the M-set image is busiest,
  i.e. points just outside the boundary. Go too far inside, and the
  corresponding Julia set is a circle; go too far outside, and it breaks
  up into scattered points. In fact, all Julia sets for C within the M-set

                     Fractint Version 15.0                     Page 22

  share the "connected" property of the M-set, and all those for C outside
  lack it.

  Fractint's spacebar toggle lets you "flip" between any view of the M-set
  and the Julia set for the point C at the center of that screen. You can
  then toggle back, or zoom your way into the Julia set for a while and
  then return to the M-set. So if the infinite complexity of the M-set
  palls, remember: each of its infinite points opens up a whole new Julia
  set.

  Historically, the Julia sets came first: it was while looking at the M-
  set as an "index" of all the Julia sets' origins that Mandelbrot noticed
  its properties.

  The relationship between the Mandelbrot set and Julia set can hold
  between other sets as well.  Many of Fractint's types are
  "Mandelbrot/Julia" pairs (sometimes called "M-sets" or "J-sets". All
  these are generated by equations that are of the form z(k+1) =
  f(z(k),c), where the function orbit is the sequence z(0), z(1), ..., and
  the variable c is a complex parameter of the equation. The value c is
  fixed for "Julia" sets and is equal to the first two parameters entered
  with the "params=Creal/Cimag" command. The initial orbit value z(0) is
  the complex number corresponding to the screen pixel. For Mandelbrot
  sets, the parameter c is the complex number corresponding to the screen
  pixel. The value z(0) is c plus a perturbation equal to the values of
  the first two parameters.  See discussion of "type=mandellambda".  This
  approach may or may not be the "standard" way to create "Mandelbrot"
  sets out of "Julia" sets.

  Some equations have additional parameters.  These values is entered as
  the third for fourth params= value for both Julia and Mandelbrot sets.
  The variables x and y refer to the real and imaginary parts of z;
  similarly, cx and cy are the real and imaginary parts of the parameter c
  and fx(z) and fy(z) are the real and imaginary parts of f(z). The
  variable c is sometimes called lambda for historical reasons.

  NOTE: if you use the "PARAMS=" argument to warp the M-set by starting
  with an initial value of Z other than 0, the M-set/J-sets correspondence
  breaks down and the spacebar toggle no longer works.


 Newton domains of attraction (type=newtbasin)

  The Newton formula is an algorithm used to find the roots of polynomial
  equations by successive "guesses" that converge on the correct value as
  you feed the results of each approximation back into the formula. It
  works very well -- unless you are unlucky enough to pick a value that is
  on a line BETWEEN two actual roots. In that case, the sequence explodes
  into chaos, with results that diverge more and more wildly as you
  continue the iteration.

  This fractal type shows the results for the polynomial Z^n - 1, which
  has n roots in the complex plane. Use the <T>ype command and enter
  "newtbasin" in response to the prompt. You will be asked for a
  parameter, the "order" of the equation (an integer from 3 through 10 --

                     Fractint Version 15.0                     Page 23

  3 for x^3-1, 7 for x^7-1, etc.). A second parameter is a flag to turn on
  alternating shades showing changes in the number of iterations needed to
  attract an orbit. Some people like stripes and some don't, as always,
  Fractint gives you a choice!

  The coloring of the plot shows the "basins of attraction" for each root
  of the polynomial -- i.e., an initial guess within any area of a given
  color would lead you to one of the roots. As you can see, things get a
  bit weird along certain radial lines or "spokes," those being the lines
  between actual roots. By "weird," we mean infinitely complex in the good
  old fractal sense. Zoom in and see for yourself.

  This fractal type is symmetric about the origin, with the number of
  "spokes" depending on the order you select. It uses floating-point math
  if you have an FPU, or a somewhat slower integer algorithm if you don't
  have one.


 Newton (type=newton)

  The generating formula here is identical to that for newtbasin, but the
  coloring scheme is different. Pixels are colored not according to the
  root that would be "converged on" if you started using Newton's formula
  from that point, but according to the iteration when the value is close
  to a root.  For example, if the calculations for a particular pixel
  converge to the 7th root on the 23rd iteration, NEWTBASIN will color
  that pixel using color #7, but NEWTON will color it using color #23.

  If you have a 256-color mode, use it: the effects can be much livelier
  than those you get with type=newtbasin, and color cycling becomes, like,
  downright cosmic. If your "corners" choice is symmetrical, Fractint
  exploits the symmetry for faster display. There is symmetry in
  newtbasin, too, but the current version of the software isn't smart
  enough to exploit it.

  The applicable "params=" values are the same as newtbasin. Try
  "params=4." Other values are 3 through 10. 8 has twice the symmetry and
  is faster. As with newtbasin, an FPU helps.


 Complex Newton (type=complexnewton/complexbasin)

  Well, hey, "Z^n - 1" is so boring when you can use "Z^a - b" where "a"
  and "b" are complex numbers!  The new "complexnewton" and "complexbasin"
  fractal types are just the old "newton" and "newtbasin" fractal types
  with this little added twist.  When you select these fractal types, you
  are prompted for four values (the real and imaginary portions of "a" and
  "b"). If "a" has a complex portion, the fractal has a discontinuity
  along the negative axis - relax, we finally figured out that it's
  *supposed* to be there!

                     Fractint Version 15.0                     Page 24

 Lambda Sets (type=lambda)

  This type calculates the Julia set of the formula lambda*Z*(1-Z). That
  is, the value Z[0] is initialized with the value corresponding to each
  pixel position, and the formula iterated. The pixel is colored according
  to the iteration when the sum of the squares of the real and imaginary
  parts exceeds 4.

  Two parameters, the real and imaginary parts of lambda, are required.
  Try 0 and 1 to see the classical fractal "dragon". Then try 0.2 and 1
  for a lot more detail to zoom in on.

  It turns out that all quadratic Julia-type sets can be calculated using
  just the formula z^2+c (the "classic" Julia"), so that this type is
  redundant, but we include it for reason of it's prominence in the
  history of fractals.


 Mandellambda Sets (type=mandellambda)

  This type is the "Mandelbrot equivalent" of the lambda set. A comment is
  in order here. Almost all the Fractint "Mandelbrot" sets are created
  from orbits generated using formulas like z(n+1) = f(z(n),C), with z(0)
  and C initialized to the complex value corresponding to the current
  pixel. Our reasoning was that "Mandelbrots" are maps of the
  corresponding "Julias". Using this scheme each pixel of a "Mandelbrot"
  is colored the same as the Julia set corresponding to that pixel.
  However, Kevin Allen informs us that the MANDELLAMBDA set appears in the
  literature with z(0) initialized to a critical point (a point where the
  derivative of the formula is zero), which in this case happens to be the
  point (.5,0). Since Kevin knows more about Dr. Mandelbrot than we do,
  and Dr. Mandelbrot knows more about fractals than we do, we defer!
  Starting with version 14 Fractint calculates MANDELAMBDA Dr.
  Mandelbrot's way instead of our way. But ALL THE OTHER "Mandelbrot" sets
  in Fractint are still calculated OUR way! (Fortunately for us, for the
  classic Mandelbrot Set these two methods are the same!)

  Well now, folks, apart from questions of faithfulness to fractals named
  in the literature (which we DO take seriously!), if a formula makes a
  beautiful fractal, it is not wrong. In fact some of the best fractals in
  Fractint are the results of mistakes! Nevertheless, thanks to Kevin for
  keeping us accurate!

  (See description of "initorbit=" command for a way to experiment with
  different orbit intializations).


 Plasma Clouds (type=plasma)

  Plasma clouds ARE real live fractals , even though we didn't know it at
  first. They are generated by a recursive algorithm that randomly picks
  colors of the corner of a rectangle, and then continues recursively
  quartering previous rectangles. Random colors are averaged with those of
  the outer rectangles so that small neighborhoods do not show much
  change, for a smoothed-out, cloud-like effect. The more colors your

                     Fractint Version 15.0                     Page 25

  video mode supports, the better.  The result, believe it or not, is a
  fractal landscape viewed as a contour map, with colors indicating
  constant elevation.  To see this, save and view with the "3" command
  (see  section on 3D), and your "cloud" will be converted to a mountain!

  You've GOT to try palette cycling on these (hit "+" or "-"). If you
  haven't been hypnotized by the drawing process, the writhing colors will
  do it for sure. We have now implemented subliminal messages to exploit
  the user's vulnerable state; their content varies with your bank
  balance, politics, gender, accessibility to a Fractint programmer, and
  so on. A free copy of Microsoft C to the first person who spots them.

  This type accepts a single parameter, which determines how abruptly the
  colors change. A value of .5 yields bland clouds, while 50 yields very
  grainy ones. The default value is 2. Zooming is ignored, as each plasma-
  cloud screen is generated randomly.

  The algorithm is based on the Pascal program distributed by Bret Mulvey
  as PLASMA.ARC. We have ported it to C and integrated it with Fractint's
  graphics and animation facilities. This implementation does not use
  floating-point math.

  Saved plasma-cloud screens are EXCELLENT starting images for fractal
  "landscapes" created with the "3D" options.


 Lambdafn (type=lambdafn)

  Function=[sin|cos|sinh|cosh|exp|log|sqr]) is specified with this type.
  Prior to version 14, these types were lambdasine, lambdacos, lambdasinh,
  lambdacos, and lambdaexp.  Where we say "lambdasine" or some such below,
  the good reader knows we mean "lambdafn with function=sin".)

  These types calculate the Julia set of the formula lambda*fn(Z), for
  various values of the function "fn", where lambda and Z are both
  complex.  Two values, the real and imaginary parts of lambda, should be
  given in the "params=" option.  For the feathery, nested spirals of
  LambdaSines and the frost-on-glass patterns of LambdaCosines, make the
  real part = 1, and try values for the imaginary part ranging from 0.1 to
  0.4 (hint: values near 0.4 have the best patterns). In these ranges the
  Julia set "explodes". For the tongues and blobs of LambdaExponents, try
  a real part of 0.379 and an imaginary part of 0.479.

  A co-processor used to be almost mandatory: each LambdaSine/Cosine
  iteration calculates a hyperbolic sine, hyperbolic cosine, a sine, and a
  cosine (the LambdaExponent iteration "only" requires an exponent, sine,
  and cosine operation)!  However, Fractint now computes these
  transcendental functions with fast integer math. In a few cases the fast
  math is less accurate, so we have kept the old slow floating point code.
  To use the old code, invoke with the float=yes option, and, if you DON'T
  have a co-processor, go on a LONG vacation!

                     Fractint Version 15.0                     Page 26

 Mandelfn (type=mandelfn)

  Function=[sin|cos|sinh|cosh|exp|log|sqr]) is specified with this type.
  Prior to version 14, these types were mandelsine, mandelcos, mandelsinh,
  mandelcos, and mandelexp. Same comment about our lapses into the old
  terminology as above!

  These are "pseudo-Mandelbrot" mappings for the LambdaFn Julia functions.
  They map to their corresponding Julia sets via the spacebar command in
  exactly the same fashion as the original M/J sets.  In general, they are
  interesting mainly because of that property (the function=exp set in
  particular is rather boring). Generate the appropriate "Mandelfn" set,
  zoom on a likely spot where the colors are changing rapidly, and hit the
  spacebar key to plot the Julia set for that particular point.

  Try "FRACTINT TYPE=MANDELFN CORNERS=4.68/4.76/-.03/.03 FUNCTION=COS" for
  a graphic demonstration that we're not taking Mandelbrot's name in vain
  here. We didn't even know these little buggers were here until Mark
  Peterson found this a few hours before the version incorporating
  Mandelfns was released.

  Note: If you created images using the lambda or mandel "fn" types prior
  to version 14, and you wish to update the fractal information in the
  "*.fra" file, simply read the files and save again. You can do this in
  batch mode via a command line like:

       "fractint oldfile.fra savename=newfile.gif batch=yes"

  For example, this procedure can convert a version 13 "type=lambdasine"
  image to a version 14 "type=lambdafn function=sin" GIF89a image.  We do
  not promise to keep this "backward compatibility" past version 14 - if
  you want to keep the fractal information in your *.fra files accurate,
  we recommend conversion.


 Barnsley Mandelbrot/Julia Sets (barnsleym1/.../j3)

  Michael Barnsley has written a fascinating college-level text, "Fractals
  Everywhere," on fractal geometry and its graphic applications. (See the
  bibliography, Appendix. D.) In it, he applies the principle of the M and
  J sets to more general functions of two complex variables.

  We have incorporated three of Barnsley's examples in Fractint. Their
  appearance suggests polarized-light microphotographs of minerals, with
  patterns that are less organic and more crystalline than those of the
  M/J sets. Each example has both a "Mandelbrot" and a "Julia" type.
  Toggle between them using the spacebar.

  The parameters have the same meaning as they do for the "regular"
  Mandelbrot and Julia. For types M1, M2, and M3, they are used to "warp"
  the image by setting the initial value of Z. For the types J1 through
  J3, they are the values of C in the generating formulas, found in
  Appendix A.

  Be sure to try the <O>rbit function while plotting these types.

                     Fractint Version 15.0                     Page 27



 Barnsley IFS Fractals (type=ifs, ifs3d)

  One of the most remarkable spin-offs of fractal geometry is the ability
  to "encode" realistic images in very small sets of numbers -- parameters
  for a set of functions that map a region of two-dimensional space onto
  itself. In principle (and increasingly in practice), a scene of any
  level of complexity and detail can be stored as a handful of numbers,
  achieving amazing "compression" ratios... how about a super-VGA image of
  a forest, more than 300,000 pixels at eight bits apiece, from a 1-KB
  "seed" file?

  Again, Michael Barnsley and his co-workers at the Georgia Institute of
  Technology are to be thanked for pushing the development of these
  iterated function systems (IFS).

  Invoking Fractint with "TYPE=ifs" defaults to an IFS "fern". Other IFS
  images can be created via the *.IFS files included with Fractint (FERN,
  TRIANGLE, TREE, and more), or from user-written files with the default
  extension *.IFS. Use the command-line argument "IFS=filename" or the
  main-menu <I> command to use or manipulate one of these files. Specify
  whether 2D or 3D (the files supplied with Fractint are almost all 2D).
  You will then be asked to pick which function to edit. Hitting <Enter>
  leaves values unchanged.

  Each line in an IFS code file contains the parameters for one of the
  generating functions, e.g. in FERN.IFS:

     a    b     c    d    e    f    p
   ___________________________________
     0     0    0  .16    0    0   .01
   .85   .04 -.04  .85    0  1.6   .85
   .2   -.26  .23  .22    0  1.6   .07
  -.15   .28  .26  .24    0  .44   .07

  The "p" values are the probabilities assigned to each function (how
  often it is used), which add up to one. Fractint supports up to 32
  functions, although usually three or four are enough.

  Note that some Barnsley IFS values generate images quite a bit smaller
  than the initial (default) screen. Just bring up the zoom box, center it
  on the small image, and hit the ENTER key to get a full-screen image.

  In order to fully appreciate the 3D fern, since your monitor is
  presumably 2D, we have added rotation, translation, and perspective
  capabilities. These share values with the same variables used in
  Fractint's other 3D facilities; for their meaning see "3D Images",
  farther on in this section. You can enter these values from the command
  line using:

  rotation=xrot/yrot/zrot       (try 30/30/30)
  shift=xshift/yshift           (shifts BEFORE applying perspective!)
  perspective=viewerposition    (try 200)

                     Fractint Version 15.0                     Page 28

  Alternatively, entering <I> from main screen and then selecting "3D
  Transform Parameters" will allow you to modify these values. The
  defaults are the same as for regular 3D, and are not always optimum for
  the 3D fern. Try rotation=30/30/30. Note that applying shift when using
  perspective changes the picture -- your "point of view" is moved.

  A truly wild variation of 3D may be seen by entering "2" for the stereo
  mode, putting on red/blue "funny glasses", and watching the fern develop
  with full depth perception right there before your eyes!

  This feature USED to be dedicated to Bruce Goren, as a bribe to get him
  to send us MORE knockout stereo slides of 3D ferns, now that we have
  made it so easy! Bruce, what have you done for us *LATELY* ?? (Just
  kidding, really!)


 Sierpinski Gasket (type=sierpinski)

  Another pre-Mandelbrot classic, this one found by W. Sierpinski around
  World War I. It is generated by dividing a triangle into four congruent
  smaller triangles, doing the same to each of them, and so on, yea, even
  unto infinity. (Notice how hard we try to avoid reiterating
  "iterating"?)

  If you think of the interior triangles as "holes", they occupy more and
  more of the total area, while the "solid" portion becomes as hopelessly
  fragile as that gasket you HAD to remove without damaging it -- you
  remember, that Sunday afternoon when all the parts stores were closed?
  There's a three-dimensional equivalent using nested tetrahedrons instead
  of triangles, but it generates too much pyramid power to be safely
  unleashed yet.

  There are no parameters for this type. We were able to implement it with
  integer math routines, so it runs fairly quickly even without an FPU.


 Quartic Mandelbrot/Julia (type=mandel4/julia4)

  These fractal types are the moral equivalent of the original M and J
  sets, except that they use the formula Z(n+1) = Z(n)^4 + C, which adds
  additional pseudo-symmetries to the plots. The "Mandel4" set maps to the
  "Julia4" set via -- surprise! -- the spacebar toggle. The M4 set is kind
  of boring at first (the area between the "inside" and the "outside" of
  the set is pretty thin, and it tends to take a few zooms to get to any
  interesting sections), but it looks nice once you get there. The Julia
  sets look nice right from the start.

  Other powers, like Z(n)^3 or Z(n)^7, work in exactly the same fashion.
  We used this one only because we're lazy, and Z(n)^4 = (Z(n)^2)^2.

                     Fractint Version 15.0                     Page 29

 Distance Estimator (distest=nnn)

  This used to be type=demm and type=demj.  These types have not died, but
  are only hiding!  They are equivalent to the mandel and julia types with
  the "distest=" option selected with a predetermined value.

  The "Distance Estimator Method" (described under "Doodads, Bells and
  Whistles") can be used to produce higher quality images of M and J sets,
  especially suitable for printing in black and white.

  If you have some *.fra files made with the old types demm/demj, you may
  want to convert them to the new form.  See "MANDELFN" section for
  directions to carry out the conversion.


 Pickover Mandelbrot/Julia Types

  (type=manfn+zsqrd/julfn+zsqrd, manzpowr/julzpowr, manzzpwr/julzzpwr,
  manfn+exp/julfn+exp - formerly included man/julsinzsqrd and
  man/julsinexp which have now been generalized)

  These types have been explored by Clifford A. Pickover, of the IBM
  Thomas J. Watson Research center. As implemented in Fractint, they are
  regular Mandelbrot/Julia set pairs that may be plotted with or without
  the "biomorph" option Pickover used to create organic-looking beasties
  (see below). These types are produced with formulas built from the
  functions z^z, z^n, sin(z), and e^z for complex z. Types with "power" or
  "pwr" in their name have an exponent value as a third parameter. For
  example, type=manzpower params=0/0/2 is our old friend the classical
  Mandelbrot, and type=manzpower params=0/0/4 is the Quartic Mandelbrot.
  Other values of the exponent give still other fractals.  Since these
  WERE the original "biomorph" types, we should give an example.  Try:

      FRACTINT type=manfn+sqrd biomorph=0 corners=-8/8/-6/6 function=sin

  to see a big biomorph digesting little biomorphs!


 Pickover Popcorn (type=popcorn/popcornjul)

  Here is another Pickover idea. This one computes and plots the orbits of
  the dynamic system defined by:

           x(n+1) = x(n) - h*sin(y(n)+tan(3*y(n))
           y(n+1) = y(n) - h*sin(x(n)+tan(3*x(n))

  with the initializers x(0) and y(0) equal to ALL the complex values
  within the "corners" values, and h=.01.  ALL these orbits are
  superimposed, resulting in "popcorn" effect.  You may want to use a
  maxiter value less than normal - Pickover recommends a value of 50.  As
  a bonus, type=popcornjul shows the Julia set generated by these same
  equations with the usual escape-time coloring. Turn on orbit viewing
  with the "O" command, and as you watch the orbit pattern you may get
  some insight as to where the popcorn comes from. Although you can zoom
  and rotate popcorn, the results may not be what you'd expect, due to the

                     Fractint Version 15.0                     Page 30

  superimposing of orbits and arbitrary use of color. Just for fun we
  added type popcornjul, which is the plain old Julia set calculated from
  the same formula.


 Peterson Variations (xxmarksxx types)

  (type=marksmandel, marksjulia, cmplxmarksmand, cmplxmarksjul)

  These fractal types are contributions of Mark Peterson. MarksMandel and
  MarksJulia are two families of fractal types that are linked in the same
  manner as the classic Mandelbrot/Julia sets: each MarksMandel set can be
  considered as a mapping into the MarksJulia sets, and is linked with the
  spacebar toggle. The basic equation for these sets is:

        Z(n+1) = ((lambda^n) * Z(n)^2) + lambda

  where Z(0) = 0.0 and lambda is (x + iy) for MarksMandel. For MarksJulia,
  Z(0) = (x + iy) and lambda is a constant (taken from the MarksMandel
  spacebar toggle, if that method is used). The exponent is a positive
  integer or a complex number. We call these "families" because each value
  of the exponent yields a different MarksMandel set, which turns out to
  be a kinda-polygon with (exponent+1) sides. The exponent value is the
  third parameter, after the "initialization warping" values. Typically
  one would use null warping values, and specify the exponent with
  something like "PARAMS=0/0/4", which creates an unwarped, pentagonal
  MarksMandel set.


 Unity (type=unity)

  This Peterson variation began with curiosity about other "Newton-style"
  approximation processes. A simple one,

     One = (x * x) + (y * y); y = (2 - One) * x;   x = (2 - One) * y;

  produces the fractal called Unity.

  One of its interesting features is the "ghost lines." The iteration loop
  bails out when it reaches the number 1 to within the resolution of a
  screen pixel. When you zoom a section of the image, the bailout
  criterion is adjusted, causing some lines to become thinner and others
  thicker.

  Only one line in Unity that forms a perfect circle: the one at a radius
  of 1 from the origin. This line is actually infinitely thin. Zooming on
  it reveals only a thinner line, up (down?) to the limit of accuracy for
  the algorithm. The same thing happens with other lines in the fractal,
  such as those around |x| = |y| = (1/2)^(1/2) = .7071

  Try some other tortuous approximations using the TEST stub (see below)
  and let us know what you come up with!

                     Fractint Version 15.0                     Page 31

 Scott Taylor / Lee Skinner Variations

  (type=fn(z*z), fn*fn, fn*z+z, fn+fn, sqr(1/fn), sqr(fn), spider,
  tetrate, manowar)

  Two of Fractint's faithful users went bonkers when we introduced the
  "formula" type, and came up with all kinds of variations on escape-time
  fractals using trig functions.  We decided to put them in as regular
  types, but there were just too many! So we defined the types with
  variable functions and let you, the, overwhelmed user, specify what the
  functions should be! Thus Scott Taylor's "z = sin(z) + z^2" formula type
  is now the "fn+fn" regular type, and EITHER function can be one of sin,
  cos, sinh, cosh, exp, log, or sqr. Plus we give you 4 parameters to set,
  the complex coefficients of the two functions!  Thus the innocent-
  looking "fn+fn" type is really at least 36 different types in disguise,
  not counting the damage done by the parameters!

  Lee informs us that you should not judge fractals by their "outer"
  appearance. For example, the images produced by z = sin(z) + z^2 and z =
  sin(z) - z^2 look very similar, but are different when you zoom in.


 Kam Torus (type=kamtorus, kamtorus3d)

  This type is created by superimposing orbits generated by a set of
  equations, with a variable incremented each time.

           x(0) = y(0) = orbit/3;
           x(n+1) = x(n)*cos(a) + (x(n)*x(n)-y(n))*sin(a)
           y(n+1) = x(n)*sin(a) - (x(n)*x(n)-y(n))*cos(a)

  After each orbit, 'orbit' is incremented by a step size. The parameters
  are angle "a", step size for incrementing 'orbit', stop value for
  'orbit', and points per orbit. Try this with a stop value of 5 with
  sound=x for some weird fractal music (ok, ok, fractal noise)! You will
  also see the KAM Torus head into some chaotic territory that Scott
  Taylor wanted to hide from you by setting the defaults the way he did,
  but now we have revealed all!

  The 3D variant is created by treating 'orbit' as the z coordinate.


 Bifurcation (type=bifxxx)

  The wonder of fractal geometry is that such complex forms can arise from
  such simple generating processes. A parallel surprise has emerged in the
  study of dynamical systems: that simple, deterministic equations can
  yield chaotic behavior, in which the system never settles down to a
  steady state or even a periodic loop. Often such systems behave normally
  up to a certain level of some controlling parameter, then go through a
  transition in which there are two possible solutions, then four, and
  finally a chaotic array of possibilities.

  This emerged many years ago in biological models of population growth.
  Consider a (highly over-simplified) model in which the rate of growth is

                     Fractint Version 15.0                     Page 32

  partly a function of the size of the current population:

  New Population =  Growth Rate * Old Population * (1 - Old Population)

  where population is normalized to be between 0 and 1. At growth rates
  less than 200 percent, this model is stable: for any starting value,
  after several generations the population settles down to a stable level.
  But for rates over 200 percent, the equation's curve splits or
  "bifurcates" into two discrete solutions, then four, and soon becomes
  chaotic.

  Type=bifurcation illustrates this model. (Although it's now considered a
  poor one for real populations, it helped get people thinking about
  chaotic systems.) The horizontal axis represents growth rates, from 190
  percent (far left) to 400 percent; the vertical axis normalized
  population values, from 0 to 4/3. Notice that within the chaotic region,
  there are narrow bands where there is a small, odd number of stable
  values. It turns out that the geometry of this branching is fractal;
  zoom in where changing pixel colors look suspicious, and see for
  yourself.

  The default display has been filtered by allowing the population to
  settle from its initial value for 5000 cycles before plotting maxiter
  population values. To override this filter value, specify a new
  (smaller) one as the first "PARAMS=" value. "PARAMS=1" produces an
  unfiltered map.

  Many formulae can be used to produce bifurcations.  Mitchel Feigenbaum
  studied lots of bifurcations in the mid-70's, using a HP-65 calculator
  (IBM PCs, Fractals, and Fractint, were all Sci-Fi then !). He studied
  where bifurcations occurred, for the formula r*p*(1-p), the one
  described above.  He found that the ratios of lengths of adjacent areas
  of bifurcation were four and a bit.  These ratios vary, but, as the
  growth rate increases, they tend to a limit of 4.669+.  This helped him
  guess where bifurcation points would be, and saved lots of time.

  When he studied bifurcations of r*sin(PI*p) he found a similar pattern,
  which is not surprising in itself.  However, 4.669+ popped out, again.
  Different formulae, same number ?  Now, THAT's surprising !  He tried
  many other formulae and ALWAYS got 4.669+ - Hot Damn !!!  So hot, in
  fact, that he phoned home and told his Mom it would make him Famous ! He
  also went on to tell other scientists.  The rest is History...

  (It has been conjectured that if Feigenbaum had a copy of Fractint, and
  used it to study bifurcations, he may never have found his Number, as it
  only became obvious from long perusal of hand-written lists of values,
  without the distraction of wild color-cycling effects !).

  We now know that this number is as universal as PI or E. It appears in
  situations ranging from fluid-flow turbulence, electronic oscillators,
  chemical reactions, and even the Mandelbrot Set - yup, fraid so:
  "budding" of the Mandelbrot Set along the negative real axis occurs at
  intervals determined by Feigenbaum's Number, 4.669201660910.....

                     Fractint Version 15.0                     Page 33

  Fractint does not make direct use of the Feigenbaum Number (YET !).
  However, it does now reflect the fact that there is a whole sub-species
  of Bifurcation-type fractals.  Those implemented to date, and the
  related formulae, (writing P for pop[n+1] and p for pop[n]) are :

    bifurcation   P =  p + r*p*(1-p)      Verhulst Bifurcations.
    biflambda     P =      r*p*(1-p)      Real equivalent of Lambda Sets.
    bif+sinpi     P =  p + r*sin(PI*p)    Population scenario based on...
    bif=sinpi     P =      r*sin(PI*p)    ...Feigenbaum's second formula.

  It took a while for bifurcations to appear here, despite them being over
  a century old, and intimately related to chaotic systems. However, they
  are now truly alive and well in Fractint!


 Lorenz Attractors (type=lorenz/lorenz3d)

  The "Lorenz Attractor" is a "simple" set of three deterministic
  equations developed by Edward Lorenz while studying the non-
  repeatability of weather patterns.  The weather forecaster's basic
  problem is that even very tiny changes in initial patterns ("the beating
  of a butterfly's wings" - the official term is "sensitive dependence on
  initial conditions") eventually reduces the best weather forecast to
  rubble.

  The lorenz attractor is the plot of the orbit of a dynamic system
  consisting of three first order non-linear differential equations. The
  solution to the differential equation is vector-valued function of one
  variable.  If you think of the variable as time, the solution traces an
  orbit.  The orbit is made up of two spirals at an angle to each other in
  three dimensions. We change the orbit color as time goes on to add a
  little dazzle to the image.  The equations are:

                  dx/dt = -a*x + a*y
                  dy/dt =  b*x - y   -z*x
                  dz/dt = -c*z + x*y

  We solve these differential equations approximately using a method known
  as the first order taylor series.  Calculus teachers everywhere will
  kill us for saying this, but you treat the notation for the derivative
  dx/dt as though it really is a fraction, with "dx" the small change in x
  that happens when the time changes "dt".  So multiply through the above
  equations by dt, and you will have the change in the orbit for a small
  time step. We add these changes to the old vector to get the new vector
  after one step. This gives us:

               xnew = x + (-a*x*dt) + (a*y*dt)
               ynew = y + (b*x*dt) - (y*dt) - (z*x*dt)
               znew = z + (-c*z*dt) + (x*y*dt)

               (default values: dt = .02, a = 5, b = 15, c = 1)

  We connect the successive points with a line, project the resulting 3D
  orbit onto the screen, and voila! The Lorenz Attractor!

                     Fractint Version 15.0                     Page 34

  We have added two versions of the Lorenz Attractor.  "Type=lorenz" is
  the Lorenz attractor as seen in everyday 2D.  "Type=lorenz3d" is the
  same set of equations with the added twist that the results are run
  through our perspective 3D routines, so that you get to view it from
  different angles (you can modify your perspective "on the fly" using the
  transformation option of the <E>ditor command.) If you set the "stereo"
  option to "2", and have red/blue funny glasses on, you will see the
  attractor orbit with depth perception.

  Hint: the default perspective values (x = 60, y = 30, z = 0) aren't the
  best ones to use for fun Lorenz Attractor viewing.  Experiment a bit -
  start with rotation values of 0/0/0 and then change to 20/0/0 and 40/0/0
  to see the attractor from different angles.- and while you're at it, use
  a non-zero perspective point Try 100 and see what happens when you get
  *inside* the Lorenz orbits.  Here comes one - Duck!  While you are at
  it, turn on the sound with the "X". This way you'll at least hear it
  coming!

  Different Lorenz attractors can be created using different parameters.
  Four parameters are used. The first is the time-step (dt). The default
  value is .02. A smaller value makes the plotting go slower; a larger
  value is faster but rougher. A line is drawn to connect successive orbit
  values.  The 2nd, third, and fourth parameters are coefficients used in
  the differential equation (a, b, and c). The default values are 5, 15,
  and 1.  Try changing these a little at a time to see the result.


 Rossler Attractors (type=rossler3D)

  This fractal is named after the German Otto Rossler, a non-practicing
  medical doctor who approached chaos with a bemusedly philosophical
  attitude.  He would see strange attractors as philosophical objects. His
  fractal namesake looks like a band of ribbon with a fold in it. All we
  can say is we used the same calculus-teacher-defeating trick of
  multiplying the equations by "dt" to solve the differential equation and
  generate the orbit.  This time we will skip straight to the orbit
  generator - if you followed what we did above with Lorenz you can easily
  reverse engineer the differential equations.

               xnew = x - y*dt -   z*dt
               ynew = y + x*dt + a*y*dt
               znew = z + b*dt + x*z*dt - c*z*dt

  Default parameters are dt = .04, a = .2, b = .2, c = 5.7


 Henon Attractors (type=henon)

  Michel Henon was an astronomer at Nice observatory in southern France.
  He came to the subject of fractals via investigations of the orbits of
  astronomical objects.  The strange attractor most often linked with
  Henon's name comes not from a differential equation, but from the world
  of discrete mathematics - difference equations. The Henon map is an
  example of a very simple dynamic system that exhibits strange behavior.
  The orbit traces out a characteristic banana shape, but on close

                     Fractint Version 15.0                     Page 35

  inspection, the shape is made up of thicker and thinner parts.  Upon
  magnification, the thicker bands resolve to still other thick and thin
  components.  And so it goes forever! The equations that generate this
  strange pattern perform the mathematical equivalent of repeated
  stretching and folding, over and over again.

               xnew =  1 + y - a*x*x
               ynew =  b*x

  The default parameters are a=1.4 and b=.3.


 Pickover Attractors (type=pickover)

  Clifford A. Pickover of the IBM Thomas J. Watson Research center is such
  a creative source for fractals that we attach his name to this one only
  with great trepidation.  Probably tomorrow he'll come up with another
  one and we'll be back to square one trying to figure out a name!

  This one is the three dimensional orbit defined by:

               xnew = sin(a*y) - z*cos(b*x)
               ynew = z*sin(c*x) - cos(d*y)
               znew = sin(x)

  Default parameters are: a = 2.24, b = .43, c = -.65, d = -2.43


 Gingerbreadman (type=gingerbreadman)

  This simple fractal is a charming example stolen from "Science of
  Fractal Images", p. 149.  Look closely, and you will see that the
  gingerbreadman contains infinitely many copies of himself at all
  different scales.

               xnew = 1 - y + |x|
               ynew = x

  There are no parameters.


 Test (type=test)

  This is a stub that we (and you!) use for trying out new fractal types.
  "Type=test" fractals make use of Fractint's structure and features for
  whatever code is in the routine 'testpt()' (located in the small source
  file TESTPT.C) to determine the color of a particular pixel.

  If you have a favorite fractal type that you believe would fit nicely
  into Fractint, just rewrite the C function in TESTPT.C (or use the
  prototype function there, which is a simple M-set implementation) with
  an algorithm that computes a color based on a point in the complex
  plane.

                     Fractint Version 15.0                     Page 36

  After you get it working, send your code to one of the authors and we
  might just add it to the next release of Fractint, with full credit to
  you. Our criteria are: 1) an interesting image and 2) a formula
  significantly different from types already supported. (Bribery may also
  work. THIS author is completely honest, but I don't trust those other
  guys.) Be sure to include an explanation of your algorithm and the
  parameters supported, preferably formatted as you see here to simplify
  folding it into the documentation.


 Formula (type=formula)

  Fractint now has a new 'type=formula' fractal type.  This is a "roll-
  your-own" fractal interpreter - you don't even need a compiler!

  To run a "type=formula" fractal, you first need a text file containing
  formulas (there's a sample file - FRACTINT.FRM - included with this
  distribution).  When you select the "formula" fractal type, you are
  prompted first for the name of your file.  Then, after the program
  locates the file and scans it for formulas, you are prompted for the
  formula name you wish to run.  After prompting for any parameters, the
  formula is parsed for syntax errors and then the fractal is generated.

  There are also two command-line options that work with type=formula
  ("formulafile=" and "formulaname=") if you are using this new fractal
  type in batch mode.

  The following documentation is supplied by Mark Peterson, who wrote the
  formula interpreter:

  Formula fractals allow you to create your own fractal formulas.  The
  general format is:

     Mandelbrot(XAXIS) { z = Pixel:  z = sqr(z) + pixel, |z| <= 4 }
        |         |          |                |              |
       Name     Symmetry    Initial         Iteration       Bailout
                            Condition                       Criteria

  Initial conditions are set, then the iterations performed until the
  bailout criteria is true or 'z' turns into a periodic loop.

  All variables are created automatically by their usage and treated as
  complex.  If you declare 'v = 2' then the variable 'v' is treated as a
  complex with an imaginary value of zero.

            Predefined Variables (x, y)
            --------------------------------------------
            z              used for periodicity checking
            p1             parameters 1 and 2
            p2             parameters 3 and 4
            pixel          screen coordinates

            Precedence
            --------------------------------------------
            1              sin(), cos(), sinh(), cosh(), sqr(),

                     Fractint Version 15.0                     Page 37

                           log(), exp(), abs(), conj(), real(),
                           imag()
            2              - (negation), ^ (power)
            3              * (multiplication), / (division)
            4              + (addition), - (subtraction)
            5              = (assignment)
            6              < (less than), <= (less than or equal to)

  Precedence may be overridden by use of parenthesis.  Note the modulus
  squared operator |z| is also parenthetic and always sets the imaginary
  component to zero.  This means 'c * |z - 4|' first subtracts 4 from z,
  calculates the modulus squared then multiplies times 'c'.  Nested
  modulus squared operators require overriding parenthesis:

            c * |z + (|pixel|)|

  The formulas are performed using either integer or floating point
  mathematics depending on the type of math you have setup.  If you do not
  have an FPU then type MPC math is performed in lieu of traditional
  floating point.

  Remember that when using integer math there is a limited dynamic range,
  so what you think may be a fractal could really be just a limitation of
  the integer math range.  God may work with integers, but His dynamic
  range is many orders of magnitude greater than our puny 32 bit
  mathematics!  Always verify with the floating point.


 Julibrots (type=julibrot)

  The following documentation is supplied by Mark Peterson, who "invented"
  the Julibrot algorithm.

  There is a very close relationship between the Mandelbrot set and Julia
  sets of the same equation.  To draw a Julia set you take the basic
  equation and vary the initial value according to the two dimensions of
  screen leaving the constant untouched.  This method diagrams two
  dimensions of the equation, 'x' and 'iy', which I refer to as the Julia
  x and y.

       z(0) = screen coordinate (x + iy)
       z(1) = (z(0) * z(0)) + c, where c = (a + ib)
       z(2) = (z(1) * z(0)) + c
       z(3) = . . . .

  The Mandelbrot set is a composite of all the Julia sets.  If you take
  the center pixel of each Julia set and plot it on the screen coordinate
  corresponding to the value of c, a + ib, then you have the Mandelbrot
  set.

       z(0) = 0
       z(1) = (z(0) * z(0)) + c, where c = screen coordinate (a + ib)
       z(2) = (z(1) * z(1)) + c
       z(3) = . . . .

                     Fractint Version 15.0                     Page 38

  I refer to the 'a' and 'ib' components of 'c' as the Mandelbrot 'x' and
  'y'.

  All the 2 dimensional Julia sets correspond to a single point on the 2
  dimensional Mandelbrot set, making a total of 4 dimensions associated
  with our equation.  Visualizing 4 dimensional objects is not as
  difficult as it may sound at first if you consider we live in a 4
  dimensional world.  The room around you is three dimensions and as you
  read this text you are moving through the fourth dimension of time. You
  and everything around your are 4 dimensional objects - which is to say 3
  dimensional objects moving through time.  We can think of the 4
  dimensions of our equation in the same manner, this is as a 3
  dimensional object evolving over time - sort of a 3 dimensional fractal
  movie.  The fun part of it is you get to pick the dimension representing
  time!

  To construct the 4 dimensional object into something you can view on the
  computer screen you start with the simple 2 dimensions of the Julia set.
  I'll treat the two Julia dimensions as the spatial dimensions of height
  and width, and the Mandelbrot 'y' dimension as the third spatial
  dimension of depth.  This leaves the Mandelbrot 'x' dimension as time.
  Draw the Julia set associated with the Mandelbrot coordinate (-.83, -
  .25), but instead of setting the color according to the iteration level
  it bailed out on, make it a two color drawing where the pixels are black
  for iteration levels less than 30, and another color for iteration
  levels greater than or equal to 30.  Now increment the Mandelbrot 'y'
  coordinate by a little bit, say (-.83, -.2485), and draw another Julia
  set in the same manner using a different color for bailout values of 30
  or greater.  Continue doing this until you reach (-.83, .25).  You now
  have a three dimensional representation of the equation at time -.83.
  If you make the same drawings for points in time before and after -.83
  you can construct a 3 dimensional movie of the equation which
  essentially is a full 4 dimensional representation.

  In the Julibrot fractal available with this release of Fractint the
  spatial dimensions of height and width are always the Julia dimensions.
  The dimension of depth is determined by the Mandelbrot coordinates.  The
  program will consider the dimension of depth as the line between the two
  Mandelbrot points.  To draw the image in our previous example you would
  set the 'From Mandelbrot' to (-.83, .25) and the 'To Mandelbrot' as (-
  .83, -.25).  If you set the number of 'z' pixels to 128 then the program
  will draw the 128 Julia sets found between Mandelbrot points (-.83, .25)
  and (-.83, -.25).  To speed things up the program doesn't actually
  calculate ALL the coordinates of the Julia sets.  It starts with the a
  pixel a the Julia set closest to the observer and moves into the screen
  until it either reaches the required bailout or the limit to the range
  of depth.  Zooming can be done in the same manner as with other
  fractals.  The visual effect (with other values unchanged) is similar to
  putting the boxed section under a pair of magnifying glasses.

  The variable associated with penetration level is the level of bailout
  there you decide to make the fractal solid.  In other words all bailout
  levels less than the penetration level are considered to be transparent,
  and those equal or greater to be opaque.  The farther away the apparent
  pixel is the dimmer the color.

                     Fractint Version 15.0                     Page 39


  The remainder of the parameters are needed to construct the red/blue
  picture so that the fractal appears with the desired depth and proper
  'z' location.  With the origin set to 8 inches beyond the screen plane
  and the depth of the fractal at 8 inches the default fractal will appear
  to start at 4 inches beyond the screen and extend to 12 inches if your
  eyeballs are 2.5 inches apart and located at a distance of 24 inches
  from the screen.  The screen dimensions provide the reference frame.

  To the human eye blue appears brighter than red.  The Blue:Red ratio is
  used to compensate for this fact.  If the image appears reddish through
  the glasses raise this value until the image appears to be in shades of
  gray.  If it appears bluish lower the ratio.  Julibrots can only be
  shown in 256 red/blue colors for viewing in either stereo-graphic
  (red/blue funny glasses) or gray-scaled.  Fractint automatically loads
  either GLASSES1.MAP or ALTERN.MAP as appropriate.


 Diffusion Limited Aggregation (type=diffusion)

  This type begins with a single point in the center of the screen.
  Subsequent points move around randomly until coming into contact with
  the first point, at which time their locations are fixed and they are
  colored randomly.  This process repeats until the fractals reaches the
  edge of the screen.  Use the show orbits function to see the points'
  random motion.

  One unfortunate problem is that on a large screen, this process will
  tend to take eons.  To speed things up, the points are restricted to a
  box around the initial point.  The first and only parameter to diffusion
  contains the size of the border between the fractal and the edge of the
  box.  If you make this number small, the fractal will look more solid
  and will be generated more quickly.

  Diffusion was inspired by a Scientific American article a couple of
  years back which includes actual pictures of real physical phenomena
  that behave like this.

  Thanks to Adrian Mariano for providing the diffusion code and
  documentation.


 Magnetic Fractals (type=magnet1m/.../magnet2j)

  These fractals use formulae derived from the study of hierarchical
  lattices, in the context of magnetic renormalisation transformations.
  This kinda stuff is useful in an area of theoretical physics that deals
  with magnetic phase-transitions (predicting at which temperatures a
  given substance will be magnetic, or non-magnetic).  In an attempt to
  clarify the results obtained for Real temperatures (the kind that you
  and I can feel), the study moved into the realm of Complex Numbers,
  aiming to spot Real phase-transitions by finding the intersections of
  lines representing Complex phase-transitions with the Real Axis.  The
  first people to try this were two physicists called Yang and Lee, who

                     Fractint Version 15.0                     Page 40

  found the situation a bit more complex than first expected, as the phase
  boundaries for Complex temperatures are (surprise!) fractals.

  And that's all the technical (?) background you're getting here!  For
  more details (are you SERIOUS ?!) read "The Beauty of Fractals".  When
  you understand it all, you might like to re-write this section, before
  you start your new job as a professor of theoretical physics...

  In Fractint terms, the important bits of the above are "Fractals",
  "Complex Numbers", "Formulae", and "The Beauty of Fractals".  Lifting
  the Formulae straight out of the Book and iterating them over the
  Complex plane (just like the Mandelbrot set) produces Fractals.

  The formulae are a bit more complicated than the Z^2+C used for the
  Mandelbrot Set, that's all.  They are :

                 /  Z^2 + (C-1)  \
      MAGNET1 : |  -------------  | ^ 2
                 \  2*Z + (C-2)  /

                 /      Z^3 + 3*(C-1)*Z + (C-1)*(C-2)      \
      MAGNET2 : |  ---------------------------------------  | ^ 2
                 \  3*(Z^2) + 3*(C-2)*Z + (C-1)*(C-2) - 1  /

  These aren't quite as horrific as they look (oh yeah ?!) as they only
  involve two variables (Z and C), but cubing things, doing division, and
  eventually squaring the result (all in Complex Numbers) don't exactly
  spell S-p-e-e-d !  These are NOT the fastest fractals in Fractint !

  As you might expect, for both formulae there is a single related
  Mandelbrot-type set (magnet1m, magnet2m) and an infinite number of
  related Julia-type sets (magnet1j, magnet2j), with the usual toggle
  between the corresponding Ms and Js via the spacebar.

  If you fancy delving into the Julia-types by hand, you will be prompted
  for the Real and Imaginary parts of the parameter denoted by C.  The
  result is symmetrical about the Real axis (and therefore the initial
  image gets drawn in half the usual time) if you specify a value of Zero
  for the Imaginary part of C.

  Fractint Historical Note:  Another complication (besides the formulae)
  in implementing these fractal types was that they all have a finite
  attractor (1.0 + 0.0i), as well as the usual one (Infinity).  This fact
  spurred the development of Finite Attractor logic in Fractint.  Without
  this code you can still generate these fractals, but you usually end up
  with a pretty boring image that is mostly deep blue "lake", courtesy of
  Fractint's standard Periodicity Checking.  See the Finite Attractors
  section for more information on this aspect of Fractint internals.

  (Thanks to Kevin Allen for Magnetic type documentation above).

                     Fractint Version 15.0                     Page 41

 L-Systems (type=lsystem)

  These fractals are constructed from line segments using rules specified
  in drawing commands.  Starting with an initial string, the axiom,
  transformation rules are applied a specified number of times, to produce
  the final command string which is used to draw the image.

  Like the type=formula fractals, this type requires a separate data file.
  A sample file, FRACTINT.L, is included with this distribution.  When you
  select type lsystem, you are asked for the filename.  Next you are asked
  for the lsystem name you wish to run.  Last, you are asked for one
  parameter - the "order", or number of times to execute all the
  transformation rules.  It is wise to start with small orders, because
  the size of the substituted command string grows exponentially and it is
  very easy to exceed your resolution.  (Higher orders take longer to
  generate too.)  The command line options "lname=" and "lfile=" can be
  used to over-ride the default file name and lsystem name.

  Each L-System entry in the file contains a specification of the angle,
  the axiom, and the transformation rules.  Each item must appear on its
  own line and each line must be less than 160 characters long.

  The statement "angle n" sets the angle to 360/n degrees; n must be an
  integer greater than two and less than fifty.

  "Axiom string" defines the axiom.

  Transformation rules are specified as "a=string" and convert the single
  character 'a' into "string."  If more than one rule is specified for a
  single character all of the strings will be added together.  This allows
  specifying transformations longer than the 160 chararacter limit.
  Transformation rules may operate on any characters except space, tab or
  '}'.

  A line which starts with ;; is a comment line.

  Here is a sample lsystem:

                   | This comment section would NOT be legal.
                   | Comments inside an L-System start with ;; at
                   | the start of the line.
  Dragon {         | Name of lsystem, { indicates start
    ;; Comment!    | This is a comment
    Angle 8        | Specify the angle increment to 45 degrees
    Axiom FX       | Starting character string
    F=             | First rule:  Delete 'F'
    y=+FX--FY+     | Change 'y' into  "+fx--fy+"
    x=-FX++FY-     | Similar transformation on 'x'
  }                | final } indicates end

  The standard drawing commands are:
      F Draw forward
      G Move forward (without drawing)
      + Increase angle
      - Decrease angle

                     Fractint Version 15.0                     Page 42

      | Try to turn 180 degrees. (If angle is odd, the turn
        will be the largest possible turn less than 180 degrees.)

  These commands increment angle by the user specified angle value. They
  should be used when possible because they are fast. If greater
  flexibility is needed, use the following commands which keep a
  completely separate angle pointer which is specified in degrees.

      D   Draw forward
      M   Move forward
      \nn Increase angle nn degrees
      /nn Decrease angle nn degrees

  Color control:
      Cnn Select color nn
      <nn Increment color by nn
      >nn decrement color by nn

  Advanced commands:
      !     Reverse directions (Switch meanings of +, - and \, /)
      @nnn  Multiply line segment size by nnn
            nnn may be a plain number, or may be preceeded by
                I for inverse, or Q for sqare root.
                (e.g.  @IQ2 divides size by the square root of 2)
      [     Push.  Stores current angle and position on a stack
      ]     Pop.  Return to location of last push

  Other characters are perfectly legal in command strings.  They are
  ignored for drawing purposes, but can be used to achieve complex
  translations.

                     Fractint Version 15.0                     Page 43

 3. Doodads, Bells, and Whistles


 Distance Estimator Method

  This is Phil Wilson's implementation of an alternate method for the M
  and J sets, based on work by mathematician John Milnor and described in
  "The Science of Fractal Images", p. 198.  While it takes full advantage
  of your color palette, one of the best uses is in preparing monochrome
  images for a printer.  Using the 1600x1200x2 disk-video mode and an HP
  LaserJet, we have produced pictures of quality equivalent to the black
  and white illustrations of the M-set in "The Beauty of Fractals."

  The distance estimator method widens very thin "strands" which are part
  of the "inside" of the set.  Instead of hiding invisibly between pixels,
  these strands are made one pixel wide.

  To turn on the distance estimator method with any escape time type
  fractal, set the "distest" value on the <X> options screen to a nonzero
  value.  You should use 1 or 2 pass mode to avoid missing some of the
  thin strands made visible by distance estimator.  For the highest
  quality, "maxiter" should also be set to a high value, say 1000 or so.
  You'll probably also want "inside" set to zero, to get a black interior.

  In color modes, this method also produces more evenly spaced contours.
  Set "distest" to a higher value for narrower color bands, a lower value
  for wider ones.  1000 is a good value to start with.

  Setting "distest" automatically toggles to floating point mode. When you
  reset distest back to zero, remember to also turn off floating point
  mode if you want it off.

  Unfortunately, images using the distance estimator method can take many
  hours to calculate even on a fast machine with a coprocessor, especially
  if a high "maxiter" value is used.  One way of dealing with this is to
  leave distest turned off while you find and frame an image.  Then hit
  <B> to save the coordinates to FRABATCH.BAT. Edit the batch file, adding
  "distest=1", "video=something" to select a high-resolution monochrome
  disk-video mode, "maxiter=1000", "inside=0" and "batch=yes".  (Watch out
  for the line exceeding the DOS limit of 120 characters - if it does, use
  "fractint @filename" in your batch and put the parameters in another
  file "filename".) Run the batch file when you won't be needing your
  machine (over the weekend?)


 Inversion

  Many years ago there was a brief craze for "anamorphic art": images
  painted and viewed with the use of a cylindrical mirror, so that  they
  looked weirdly distorted on the canvas but correct in the distorted
  reflection. (This byway of art history may be a useful defense when your
  friends and family give you odd looks for staring at fractal images
  color-cycling on a CRT.)

                     Fractint Version 15.0                     Page 44

  The Inversion option performs a related transformation on most of the
  fractal types. You define the center point and radius of a circle;
  Fractint maps each point inside the circle to a corresponding point
  outside, and vice-versa. This is known to mathematicians as inverting
  (or if you want to get precise, "everting") the plane, and is something
  they can contemplate without getting a headache. John Milnor, mentioned
  earlier in connection with the distance-estimator method, made his name
  in the 1950s with a method for everting a seven-dimensional sphere, so
  we have a lot of catching up to do.

  For example, if a point inside the circle is 1/3 of the way from the
  center to the radius, it is mapped to a point along the same radial
  line, but at a distance of (3 * radius) from the origin. An outside
  point at 4 times the radius is mapped inside at 1/4 the radius.

  The inversion parameters on the <Y> options screen allow entry of the
  radius and center coordinates of the inversion circle. A default choice
  of -1 sets the radius at 1/6 the smaller dimension of the image
  currently on the screen.  The default values for Xcenter and Ycenter use
  the coordinates currently mapped to the center of the screen.

  Try this one out with a Newton plot, so its radial "spokes" will give
  you something to hang on to. Plot a Newton-method image, then set the
  inversion radius to 1, with default center coordinates. The center
  "explodes" to the periphery.

  Inverting through a circle not centered on the origin produces bizarre
  effects that we're not even going to try to describe. Aren't computers
  wonderful?


 Decomposition

  You'll remember that most fractal types are calculated by iterating a
  simple function of a complex number, producing another complex number,
  until either the number exceeds some pre-defined "bailout" value, or the
  iteration limit is reached. The pixel corresponding to the starting
  point is then colored based on the result of that calculation.

  The decomposition option ("decomp=", on the <X> screen) toggles to
  another coloring protocol.  Here the points are colored according to
  which quadrant of the complex plane (negative real/positive imaginary,
  positive real/positive imaginary, etc.) the final value is in. If you
  use 4 as the parameter, points ending up in each quadrant are given
  their own color; if 2 (binary decomposition), points in alternating
  quadrants are given 2 alternating colors.

  The result is a kind of warped checkerboard coloring, even in areas that
  would ordinarily be part of a single contour. Remember, for the M-set
  all points whose final values exceed 2 (by any amount) after, say, 80
  iterations are normally the same color; under decomposition, Fractint
  runs [bailout-value] iterations and then colors according to where the
  actual final value falls on the complex plane.

                     Fractint Version 15.0                     Page 45

  When using decomposition, a higher bailout value will give a more
  accurate plot, at some expense in speed.  You might want to set the
  bailout value (in the parameters prompt following selection of a new
  fractal type; present for most but not all types) to a higher value than
  the default.  A value of about 50 is a good compromise for M/J sets.


 Logarithmic Palettes

  By default, Fractint maps iterations to colors 1-1.  If you are using a
  16-color video mode, and you are using the default maximum iteration
  count of 150, your image will run through the 16-color palette 150/16 =
  9.375 times.  If you elect to use Logarithmic palettes, the entire range
  of iteration values is compressed to map to one span of the color range.
  This results in spectacularly different images if you are using a high
  iteration limit near the current iteration maximum of 32000 and are
  zooming in on an area near a "lakelet".

  Fractint has a number of types of compressed palette, selected by the
  "Log Palette" line on the <X> screen, or by the "logmap=" command line
  parameter.

  logmap=1: for standard logarithmic palette.

  logmap=-1: "old" logarithmic palette. This variant was the only one used
  before Fractint 14.0. It differs from logmap=1 in that some colors are
  not used - logmap=1 "spreads" low color numbers which are unused by
  logmap=-1's pure logarithmic mapping so that all colors are assigned.

  logmap=N (>1): Same as logmap=1, but starting from iteration count N.
  Pixels with iteration counts less than N are mapped to color 1. This is
  useful when zooming in an area near the lake where no points in the
  image have low iteration counts - it makes use of the low colors which
  would otherwise be unused.

  logmap=-N (<-1): Similar to logmap=N, but uses a square root
  distribution of the colors instead of a logarithmic one.

  When using a compressed palette in a 256 color mode, we suggest changing
  your colors from the usual defaults.  The last few colors in the default
  IBM VGA color map are black.  This results in points nearest the "lake"
  smearing into a single dark band, with little contrast from the blue (by
  default) lake.


 Biomorphs

  Related to binary decomposition are the "biomorphs" invented by Clifford
  Pickover, and discussed by A. K. Dewdney in the July 1989 "Scientific
  American", page 110.  These are so-named because this coloring scheme
  makes many fractals look like one-celled animals.  The idea is simple.
  The escape-time algorithm terminates an iterating formula when the size
  of the orbit value exceeds a predetermined bailout value. Normally the
  pixel corresponding to that orbit is colored according to the iteration
  when bailout happened. To create biomorphs, this is modified so that if

                     Fractint Version 15.0                     Page 46

  EITHER the real OR the imaginary component is LESS than the bailout,
  then the pixel is set to the "biomorph" color. The effect is a bit
  better with higher bailout values: the bailout is automatically set to
  100 when this option is in effect. You can try other values with the
  "bailout=" option.

  The biomorph option is turned on via the "biomorph=nnn" command-line
  option (where "nnn" is the color to use on the affected pixels).  When
  toggling to Julia sets, the default corners are three times bigger than
  normal to allow seeing the biomorph appendages. Does not work with all
  types - in particular it fails with any of the mandelsine family.
  However, if you are stuck with monochrome graphics, try it - works great
  in two-color modes. Try it with the marksmandel and marksjulia types.


 Starfields

  Once you have generated your favorite fractal image, you can convert it
  into a fractal starfield with the 'a' transformation (for 'astronomy'? -
  once again, all of the good letters were gone already).  Stars are
  generated on a pixel-by-pixel basis - the odds that a particular pixel
  will coalesce into a star are based (partially) on the color index of
  that pixel.

  (The following was supplied by Mark Peterson, the starfield author).

  If the screen were entirely black and the 'Star Density per Pixel' were
  set to 30 then a starfield transformation would create an evenly
  distributed starfield with an average of one star for every 30 pixels.

  If you're on a 320x200 screen then you have 64000 pixels and would end
  up with about 2100 stars.  By introducing the variable of 'Clumpiness'
  we can create more stars in areas that have higher color values.  At
  100% Clumpiness a color value of 255 will change the average of finding
  a star at that location to 50:50.  A lower clumpiness values will lower
  the amount of probability weighting.  To create a spiral galaxy draw
  your favorite spiral fractal (IFS, Julia, or Mandelbrot) and perform a
  starfield transformation.  For general starfields I'd recommend
  transforming a plasma fractal.

  Real starfields have many more dim stars than bright ones because very
  few stars are close enough to appear bright.  To achieve this effect the
  program will create a bell curve based on the value of ratio of Dim
  stars to bright stars.  After calculating the bell curve the curve is
  folded in half and the peak used to represent the number of dim stars.

  Starfields can only be shown in 256 colors.  Fractint will automatically
  try to load ALTERN.MAP and abort if the map file cannot be found.

                     Fractint Version 15.0                     Page 47

 4. "3D" Images

  Fractint can now restore images in "3D". Important: we use quotation
  marks because it does not CREATE images of 3D fractal objects (there are
  such, but we're not there yet.) Instead, it restores .GIF images as a 3D
  PROJECTION or STEREO IMAGE PAIR.  The iteration values you've come to
  know and love, the ones that determine pixel colors, are translated into
  "height" so that your saved screen becomes a landscape viewed in
  perspective. You can even wrap the landscape onto a sphere for
  realistic-looking planets and moons that never existed outside your PC!

  We suggest starting with a saved plasma-cloud screen. Hit <3> in main
  command mode to begin the process. Next, select the file to be
  transformed, and the video mode. (Usually you want the same video mode
  the file was generated in; other choices may or may not work.)

  Now, you'll be bombarded with a long series of options. Not to worry:
  all of them have defaults chosen to yield an acceptable starting image,
  so the first time out just pump your way through with the <Enter> key.
  When you enter a different value for any option, that becomes the
  default value the next time you hit <3>, so you can change one option at
  a time until you get what you want. Generally <ESC> will take you back
  to the previous screen.

  Once you're familiar with the effects of the 3D option values you have a
  variety of options on how to specify them. You can specify them all on
  the command line (there ARE a lot of them so they may not all fit within
  the DOS command line limits), with an SSTOOLS.INI file, or with a
  command file.

  Here's an example for you power FRACTINTers, the command

            FRACTINT MYFILE SAVENAME=MY3D 3D=YES BATCH=YES

  would make Fractint load MYFILE.GIF, re-plot it as a 3D landscape
  (taking all of the defaults), save the result as MY3D.GIF, and exit to
  DOS. By the time you've come back with that cup of coffee, you'll have a
  new world to view, if not conquer.

  Note that the image created by 3D transformation is treated as if it
  were a plasma cloud - We have NO idea how to retain the ability to zoom
  and pan around a 3D image that has been twisted, stretched, perspective-
  ized, and water-leveled. Actually, we do, but it involves the kind of
  hardware that Industrial Light & Magic, Pixar et al. use for feature
  films. So if you'd like to send us a check equivalent to George Lucas'
  net from the "Star Wars" series...


 3D Mode Selection

  After hitting <3> and getting past the filename prompt and video mode
  selection, you're presented with a "3d Mode Selection" screen. Each
  selection will have defaults entered if you wish to change any of the
  defaults use the cursor keys to move through the menu. When you're
  satisfied press <Enter>.

                     Fractint Version 15.0                     Page 48


  Here are the options and what they do:

  Preview Mode:

     Preview mode provides a rapid look at your transformed image using
     by skipping a lot of rows and filling the image in. Good for quickly
     discovering the best parameters. Let's face it, the Fractint authors
     most famous for "blazingly fast" code *DIDN'T* write the 3D
     routines!

  Show Box:

     If you have selected Preview Mode you have another option to worry
     about. This is the option to show the image box in scaled and
     rotated coordinates x, y, and z. The box only appears in rectangular
     transformations and shows how the final image will be oriented. If
     you select light source in the next screen, it will also show you
     the light source vector so you can tell where the light is coming
     from in relation to your image. Sorry no head or tail on the vector
     yet.

  Coarseness:

     This sets how many divisions the image will be divided into in the y
     direction, if you select preview mode above, or grid fill in the
     "Select Fill Type" screen next.

  Spherical Projection:

     The next question asks if you want a sphere projection. This will
     take  your image and map it onto a plane if you answer "no" or a
     sphere if you answer "yes" as described above. Try it and you'll see
     what we mean.

  Stereo:

     Stereo sound in Fractint? Well, not yet. Fractint now allows you to
     create 3D images for use with red/blue glasses like 3D comics you
     may have seen, or images like Captain EO.

     Option 0 is normal old 3D you can look at with just your eyes.

     Options 1 and 2 require the special red/blue-green glasses.  They
     are meant to be viewed right on the screen or on a color print off
     of the screen. The image can be made to hover entirely or partially
     in front of the screen. Great fun!  These two options give a gray
     scale image when viewed.

     Option 1 gives 64 shades of gray but with half the spatial
     resolution you have selected. It works by writing the red and blue
     images on adjacent pixels, which is why it eats half your
     resolution. In general, we recommend you use this only with
     resolutions above 640x350. Use this mode for continuous potential
     landscapes where you *NEED* all those shades.

                     Fractint Version 15.0                     Page 49


     Option "2" gives you full spatial resolution but with only 16 shades
     of gray. If the red and blue images overlap, the colors are mixed.
     Good for wire-frame images (we call them surface grids), lorenz3d
     and ifs3d. Works fine in 16 color modes.

     Option 3 is for creating stereo pair images for view later with more
     specialized equipment. It allows full color images to be presented
     in glorious stereo. The left image presented on the screen first.
     You may photograph it or save it. Then the second image is
     presented, you may do the same as the first image. You can then take
     the two images and convert them to a stereo image pair as outlined
     by Bruce Goren (see below). When you are satisfied with your
     selections press enter to go to the next screen which will appear
     below this one.


 Select Fill Type Screen

  These options exist because in the course of the 3D projection, portions
  of the original image may be stretched to fit the new surface. Points of
  an image that formerly were right next to each other, now may have a
  space between them. These options generally determine what to do with
  the space between the mapped dots.

  For an illustration, pick the second option "just draw the points",
  which just maps points to corresponding points. Generally this will
  leave empty space between many of the points. Therefore you can choose
  various algorithms that "fill in" the space between the points in
  various ways.

  Now, try the first option "make a surface grid." This option will make a
  grid of the surface which is as many divisions in the original "y"
  direction as was set in "coarse" in the first screen. It is very fast,
  and can give you a good idea what the final relationship of parts of
  your picture will look like.

  Try the second option, "connect the dots (wire frame)", then "surface
  fills - (colors interpolated)" and "(colors not interpolated), the
  general favorite of the authors. Solid fill, while it reveals the
  pseudo-geology under your pseudo-landscape, inevitably takes longer.

  Now try the light source fill types. These two algorithms allow you to
  position the "sun" over your "landscape." Each pixel is colored
  according to the angle the surface makes with an imaginary light source.
  You will be asked to enter the three coordinates of the vector pointing
  toward the light in one of the following screens.

  Light source before transformation calculates the illumination before
  doing the coordinate transformations, and is slightly faster. If you
  generate a sequence of images where one rotation is progressively
  changed, the effect is as if the image and the light source are fixed in
  relation to each other and you orbit around the image.

                     Fractint Version 15.0                     Page 50

  Light source after transformation applies the transformations first,
  then calculates the illumination. If you generate a sequence of images
  with progressive rotation as above the effect is as if you and the light
  source are fixed and the object is rotating.

  For ease of discussion we will refer to the following fill types by
  these numbers:
      1 - surface grid
      2 - (default) - no fill at all - just draw the dots.
      3 - wire frame - joins points with lines
      4 - surface fill - (colors interpolated)
      5 - surface fill - (interpolation turned off)
      6 - solid fill - draws lines from the "ground" up to the point
      7 - surface fill with light model - calculated before 3D transforms
      8 - surface fill with light model - calculated after 3D transforms

  Types 4, 7, and 8 interpolate colors when filling, making a very smooth
  fill if the palette is continuous. This may not be desirable if the
  palette is not continuous. Type 5 is the same as type 4 with
  interpolation turned off. You might want to use fill type 5, for
  example, to project a .GIF photograph onto a sphere. With type 4, you
  might see the filled-in points, since chances are the palette is not
  continuous; type 5 fills those same points in with the colors of
  adjacent pixels. However, for most fractal images, fill type 4 works
  better.


 Stereo 3D Viewing

  If you selected Stereo option 1, 2 or 3 you will be presented another
  screen to select from. We suggest you definitely use defaults at first
  on this one.

  Funny Glasses Parameters

  When you look at an image with both eyes, each eye sees the image in
  slightly different perspective because they see it from different
  places.

  The first selection you must make is ocular separation, the distance the
  between the viewers eyes. This is measured as a % of screen and is an
  important factor in setting the position of the final stereo image in
  front of or behind the CRT Screen.

  The second selection is convergence, also as a % of screen. This tends
  to move the image forward and back to set where it floats. More positive
  values move the image towards the viewer. The value of this parameter
  needs to be set in conjunction with the setting of ocular separation and
  the perspective distance. It directly adjusts the overall separation of
  the two stereo images. Beginning anaglyphers love to create images
  floating mystically in front of the screen, but grizzled old 3D veterans
  look upon such antics with disdain, and believe the image should be
  safely inside the monitor where it belongs!

                     Fractint Version 15.0                     Page 51

  Left and Right Red and Blue image crop (% of screen also) help keep the
  visible part of the right image the same as the visible part of the left
  by cropping them. If there is too much in the field of either eye that
  the other doesn't see, the stereo effect can be ruined.

  Red and Blue brightness factor. The generally available red/blue-green
  glasses, made for viewing on ink on paper and not the light from a CRT,
  let in more red light in the blue-green lens than we would like. This
  leaves a ghost of the red image on the blue-green image (definitely not
  desired in stereo images). We have countered this by adjusting the
  intensity of the red and blue values on the CRT. In general you should
  not have to adjust this.

  The final entry is Map file name. If you have a special map file you
  want to use for Stereo 3D this is the place to enter its name. Generally
  glasses1.map is for type 1 (alternating pixels), and glasses2.map is for
  type 2 (superimposed pixels). Grid.map is great for wire-frame images
  using 16 color modes.


 Rectangular Coordinate Transformation

  The first entries are rotation values around the X, Y, and Z axes. Think
  of your starting image as a flat map: the X value tilts the bottom of
  your monitor towards you by X degrees, the Y value pulls the left side
  of the monitor towards you, and the Z value spins it counter-clockwise.
  Note that these are NOT independent rotations: the image is rotated
  first along the X-axis, then along the Y-axis, and finally along the Z-
  axis. Those are YOUR axes, not those of your (by now hopelessly skewed)
  monitor. All rotations actually occur through the center of the original
  image.

  Then there are three scaling factors in percent. Initially, leave the X
  and Y axes alone and play with Z, now the vertical axis, which
  translates into surface "roughness."  High values of Z make spiky, on-
  beyond-Alpine mountains and improbably deep valleys; low values make
  gentle, rolling terrain. Negative roughness is legal: if you're doing an
  M-set image and want Mandelbrot Lake to be below the ground, instead of
  eerily floating above, try a roughness of about -30%.

  Next we need a water level -- really a minimum-color value that performs
  the function "if (color < waterlevel) color = waterlevel". So it plots
  all colors "below" the one you choose at the level of that color, with
  the effect of filling in "valleys" and converting them to "lakes."

  Now we enter a perspective distance, which you can think of as the
  "distance" from your eye to the image. A zero value (the default) means
  no perspective calculations, which allows use of a faster algorithm.

  For non-zero values, picture a box with the original X-Y plane of your
  flat fractal on the bottom, and your 3D fractal inside. A perspective
  value of 100% places your eye right at the edge of the box and yields
  fairly severe distortion, like a close view through a wide-angle lens.
  200% puts your eye as far from the front of the box as the back is
  behind. 300% puts your eye twice as far from the front of the box as the

                     Fractint Version 15.0                     Page 52

  back is, etc. Try about 150% for reasonable results. Much larger values
  put you far away for even less distortion, while values smaller than
  100% put you "inside" the box. Try larger values first, and work your
  way in.

  Next, you are prompted for two types of X and Y shifts (now back in the
  plane of your screen) that let you move the final image around if you'd
  like to re-center it. The first set, x and y shift with perspective,
  move the image and the effect changes the perspective you see. The
  second set, "x and y adjust without perspective", move the image but do
  not change perspective.  They are used just for positioning the final
  image on the screen.


 Color Parameters

  Now, you are asked for a range of "transparent" colors, if any. This
  option is most useful when using the <O>verlay command below. Enter the
  color range (minimum and maximum value) for which you do not want to
  overwrite whatever may already be on the screen. The default is no
  transparency (overwrite everything).

  Now, for the final option. This one will smooth the transition between
  colors by randomizing them and reduce the banding that occurs with some
  maps. Select the value of randomize to between 0 (for no effect) and 7
  (to randomize your colors almost beyond use). 3 is a good starting
  point.

  Well, OK, we lied. If you selected one of the light source fill options,
  there are still MORE options.

  If you have selected a fill type which uses light source, you can select
  the final image to be either in monochrome or full color. 0 selects
  monochrome and 1 selects glorious full color.

  That's all for this screen. Press enter and the next and final screen
  will appear (honestly!).


 Light Source Parameters

  This one deals with all the aspects of light source.

  You must chose the direction of the light from the light source. This
  will be scaled in the x, y, and z directions the same as the image. For
  example, 1,1,3 positions the light to come from the lower right front of
  the screen in relation to the untransformed image. It is important to
  remember that these coordinates are scaled the same as your image. Thus,
  "1,1,1" positions the light to come from a direction of equal distances
  to the right, below and in front of each pixel on the original image.
  However, if the x,y,z scale is set to 90,90,30 the result will be from
  equal distances to the right and below each pixel but from only 1/3 the
  distance in front of the screen i.e.. it will be low in the sky, say,
  afternoon or morning.

                     Fractint Version 15.0                     Page 53

  Then you are asked for a smoothing factor. Unless you used continuous
  potential (see chapter 6) when generating the starting image, the
  illumination when using light source fills may appear "sparkly", like a
  sandy beach in bright sun. A smoothing factor of 2 or 3 will allow you
  to see the large-scale shapes better.

  This is primarily useful when doing light source fill types with plasma
  clouds. But if your fractal is not a plasma cloud and has features with
  sharply defined boundaries (e.g. Mandelbrot Lake), the smoothing may
  cause the colors to run. This is a feature, not a bug. (A copyrighted
  response of [your favorite commercial software company here], used by
  permission.)

  The ambient option sets the minimum light value a surface has if it has
  no direct lighting at all. All light values are scaled from this value
  to white. This effectively adjusts the depth of the shadows and sets the
  overall contrast of the image.

  If you selected the full color option, you have a few more choices. The
  next is the haze factor. Set this to make distant objects more hazy.
  Close up objects will have little effect, distant objects will have
  most. 0 disables the function. 100 is the maximum effect, the farthest
  objects will be lost in the mist. Currently, this does not really use
  distance from the viewer, we cheat and use the y value of the original
  image. So the effect really only works if the y-rotation (set earlier)
  is between +/- 30.

  Finally, absolutely the last option (this time we mean it): you can
  chose the name under which to save your light file. If you have a RAM
  disk handy, you might want to create the file on it for speed, so
  include its full path name in this option. If you have not set
  "overwrite=yes" then the file name will be incremented to avoid over-
  writing previous files. By the way, the background on the full color
  file is sky blue instead of black.

  You'll probably want to adjust the final colors for monochrome fill
  types using light source via color cycling. Try one of the more
  continuous palettes (<F8> through <F10>), or load the GRAY palette with
  the <A>lternate-map command.

  Now, lie down for a while in a quiet room with a damp washcloth on your
  forehead. Feeling better? Good -- because it's time to go back almost to
  the top of the 3D options and just say yes to:


 Spherical Projection

  Picture a globe lying on its side, "north" pole to the right. (It's our
  planet, and we'll position it the way we like.) You will be mapping the
  X and Y axes of the starting image to latitude and longitude on the
  globe, so that what was a horizontal row of pixels follows a line of
  longitude. The defaults exactly cover the hemisphere facing you, from
  longitude 180 degrees (top) to 0 degrees (bottom) and latitude -90
  (left) to latitude 90 (right). By changing them you can map the image to
  a piece of the hemisphere or wrap it clear around the globe.

                     Fractint Version 15.0                     Page 54


  The next entry is for a radius factor that controls the over-all size of
  the globe. All the rest of the entries are the same as in the landscape
  projection. You may want less surface roughness for a plausible look,
  unless you prefer small worlds with big topography, a la "The Little
  Prince."

  WARNING: When the "construction" process begins at the edge of the globe
  (default) or behind it, it's plotting points that will be hidden by
  subsequent points as the process sweeps around the sphere toward you.
  Our nifty hidden-point algorithms "know" this, and the first few dozen
  lines may be invisible unless a high mountain happens to poke over the
  horizon. If you start a spherical projection and the screen stays black,
  wait for a while (a longer while for higher resolution or fill type 6)
  to see if points start to appear. Would we lie to you? If you're still
  waiting hours later, first check that the power's still on, then
  consider a faster system.


 3D Overlay Mode

  While the <3> command creates its image on a blank screen, the <O>
  command draws a second image over an existing displayed image. This
  image can be any restored image from a <R> command or the result of a
  just executed <3> command. So you can do a landscape, then hit <O> and
  choose spherical projection to re-plot that image or another as a moon
  in the sky above the landscape. <O> can be repeated as many times as you
  like.

  It's worth noting that not all that many years ago, one of us watched
  Benoit Mandelbrot and fractal-graphics wizard Dick Voss creating just
  such a moon-over-landscape image at IBM's research center in Yorktown
  Heights, NY. The system was a large and impressive mainframe with
  floating-point facilities bigger than the average minicomputer, running
  LBLGRAPH -- what Mandelbrot calls "an independent-minded and often very
  ill-mannered heap of graphics programs that originated in work by Alex
  Hurwitz and Jack Wright of IBM Los Angeles."

  We'd like to salute LBLGRAPH, its successors, and their creators,
  because it was their graphic output (like "Planetrise over Labelgraph
  Hill," plate C9 in Mandelbrot's "Fractal Geometry of Nature") that
  helped turn fractal geometry from a mathematical curiosity into a
  phenomenon. We'd also like to point out that it wasn't as fast, flexible
  or pretty as Fractint on a 386/16 PC with S-VGA graphics. Now, a lot of
  the difference has to do with the incredible progress of micro-processor
  power since then, so a lot of the credit should go to Intel rather than
  to our highly tuned code. OK, twist our arms -- it IS awfully good code.


 Special Note for CGA or Hercules Users

  If you are one of those unfortunates with a CGA or Hercules 2-color
  monochrome graphics, it is now possible for you to make 3D projection
  images.

                     Fractint Version 15.0                     Page 55

  Try the following unfortunately circuitous approach. Invoke Fractint,
  making sure you have set askvideo=yes. Use a diskvideo mode to create a
  256 color fractal. You might want to edit the fractint.cfg file to make
  a diskvideo mode with the same pixel dimensions as your normal video
  (see "batch=config" command for how to create fractint.cfg). Using the
  "3" command, enter the file name of the saved 256 color file, say "no"
  to the "Legal for this machine?" prompt, selecting instead your 2 or 4
  color mode, and answer the other 3D prompts. You will then see a 3D
  projection of the fractal. Another example of Stone Soup responsiveness
  to our fan mail!


 Making Terrains

  If you enjoy using Fractint for making landscapes, we now have several
  new features for you to work with. When doing 3d transformations banding
  tends to occur because all pixels of a given height end up the same
  color. Now, colors can be randomized to make the transitions between
  different colors at different altitudes smoother. Use the new
  "RANDOMIZE= " variable to accomplish this. If your light source images
  all look like lunar landscapes since they are all monochrome and have
  very dark shadows, we now allow you to set the ambient light for
  adjusting the contrast of the final image. Use the "Ambient= " variable.
  In addition to being able to create scenes with light sources in
  monochrome, you can now do it in full color as well. Setting fullcolor=1
  will generate a Targa-24 file with a full color image which will be a
  combination of the original colors of the source image (or map file if
  you select map=something) and the amount of light which reflects off a
  given point on the surface. Since there can be 256 different colors in
  the original image and 256 levels of light, you can now generate an
  image with *lots* of colors. To convert it to a GIF if you can't view
  Targa files directly, you can use PICLAB (see Appendix E for information
  about getting PICLAB), and the following commands:

      SET PALETTE 256
      SET CREZ 8
      TLOAD yourfile.tga
      MAKEPAL
      MAP
      GSAVE yourfile.gif
      EXIT
  Using the full color option allows you to also set a haze factor with
  the "haze= " variable to make more distant objects more hazy.

  As a default, full color files also have the background set to sky blue.
  Warning, the files which are created with the full color option are very
  large, 3 bytes per pixel. So make sure to use a disk with enough space.
  The file is created using Fractint's disk-video caching, but is always
  created on real disk (expanded or extended memory is not used.) Try the
  following settings of the new variables in sequence to get a feel for
  the effect of each one:
      ;use this with any filltype
      map=topo
      randomize=3; adjusting this smooths color transitions

                     Fractint Version 15.0                     Page 56

      ;now add this using filltype 5 or 6
      ambient=20; adjusting this changes the contrast
      filltype=6
      smoothing=2; makes the light not quite as granular as the terrain

      ;now add the following, and this is where it gets slow
      fullcolor=1; use PICLAB to reduce resulting lightfile to a GIF

      ;and finally this
      haze=20; sets the amount of haze for distant objects

  When full color is being used, the image you see on the screen will
  represent the amount of light being reflected, not the colors in the
  final image. Don't be disturbed if the colors look weird, they are an
  artifact of the process being used. The image being created in the
  lightfile won't look like the screen.

  However, if you are worried, hit ESC several times and when Fractint
  gets to the end of the current line it will abort. Your partial image
  will be there as LIGHT001.TGA or with whatever file name you selected
  with the lightname option. Convert it as described above and adjust any
  parameters you are not happy with. Its a little awkward, but all we
  haven't figured out a better way yet.


 Making 3D Slides

  Bruce Goren, CIS's resident stereoscopic maven, contributed these tips
  on what to do with your 3D images (Bruce inspired and prodded us so much
  we automated much of what follows, allowing both this and actual on
  screen stereo viewing, but we included it here for reference and a brief
  tutorial.)

  "I use a Targa 32 video card and TOPAS graphic software, moving the
  viewport or imaginary camera left and right to create two separate views
  of the stationary object in x,y,z, space. The distance between the two
  views, known as the inter-ocular distance, toe-in or convergence angle,
  is critical. It makes the difference between good 3-D and headache-
  generating bad 3-D.

  "For a 3D fractal landscape, I created and photographed the left and
  right eye views as if flying by in an imaginary airplane and mounted the
  film chips for stereo viewing. To make my image, first I generated a
  plasma cloud based on a color map I calculated to resemble a geological
  survey map (available on CIS as TARGA.MAP). In the 3D reconstruction, I
  used a perspective value of 150 and shifted the camera -15 and +15 on
  the X-axis for the left and right views. All other values were left to
  the defaults.

  "The images are captured on a Matrix 3000 film recorder -- basically a
  box with a high-resolution (1400 lines) black and white TV and a 35mm
  camera (Konica FS-1) looking at the TV screen through a filter wheel.
  The Matrix 3000 can be calibrated for 8 different film types, but so far
  I have only used Kodak Ektachrome 64 daylight for slides and a few print
  films. I glass mount the film chips myself.

                     Fractint Version 15.0                     Page 57


  "Each frame is exposed three times, once through each of the red, blue,
  and green filters to create a color image from computer video without
  the scan-lines which normally result from photographing television
  screens.  The aspect ratio of the resulting images led me to mount the
  chips using the 7-sprocket Busch-European Emde masks. The best source of
  Stereo mounting and viewing supplies I know of is an outfit called Reel
  3-D Enterprises, Inc. at P.O. Box 2368, Culver City, CA 90231, tel. 213-
  837-2368. "My platform is an IBM PC/AT crystal-swapped up to 9 MHz. The
  math co-processor runs on a separate 8-MHz accessory sub-board.  The
  system currently has 6.5 MB of RAM."

                     Fractint Version 15.0                     Page 58

 5. Command-Line Parameters, Setting Defaults, Batch Mode


  Fractint accepts command-line arguments that allow you to load it with
  your own choice of video mode, starting coordinates, and just about
  every other parameter and option. These arguments can also be included
  in a SSTOOLS.INI startup file, or in command files invoked from the
  command line using a command like "FRACTINT @MYFILE". Fractint first
  looks along the DOS PATH for any file called SSTOOLS.INI and reads
  start-up variables from that file. Then, it looks at its own command
  line; arguments which will over-ride those from the .INI file. General
  syntax is:

                FRACTINT argument argument argument...

  where the individual arguments are separated by one or more spaces (an
  individual argument may NOT include spaces). Either upper or lower case
  may be used, and arguments can be in any order. In an SSTOOLS.INI file
  you may replace the spaces with Returns.

  Some terminology:
  COMMAND=nnn               enter a number in place of "nnn"
  COMMAND=[filename]        you supply filename
  COMMAND=yes|no|whatever   choose one of "yes", "no", and "whatever"
  COMMAND=1st[/2nd[/3rd]] - the slash-separated parameters "2nd" and
                            "3rd" are optional


 General Parameters

  @FILENAME
  Causes Fractint to read "filename" for arguments. When it finishes, it
  resumes reading its own command line -- i.e., "FRACTINT MAXITER=250
  @MYFILE PASSES=1" is legal. This option is only valid on the command
  line, as Fractint is not clever enough to deal with multiple
  indirection.

  FILENAME=[name]
  Causes Fractint to read the named file, which must either have been
  saved from an earlier Fractint session (version 7.0 or later) or be a
  generic GIF file, and use that as the starting point, bypassing the
  initial information screens. The filetype is optional and defaults to
  .GIF. Non-Fractint GIF files are restored as fractal type "plasma". On
  the command line you may omit FILENAME= and just give the name; the full
  argument is required in SSTOOLS.INI.

  TYPE=[name]
  Selects the type of fractal image to display. The default is type
  "mandel," the M-set.

  PARAMS=n/n/n/n...
  Set optional (required, for some fractal types) values used in plotting.
  These numbers typically represent the real and imaginary portions of
  some startup value, and are described in detail as needed in chapter 2.

                     Fractint Version 15.0                     Page 59

  (Example: FRACTINT TYPE=julia PARAMS=-0.48/0.626 would wait at the
  opening screen for you to select a video mode, but then proceed straight
  to the Julia set for the stated x (real) and y (imaginary) coordinates.)

  CORNERS=xmin/xmax/ymin/ymax[/x3rd/y3rd]
  Example: corners=-0.739/-0.736/0.288/0.291
  Begin with these coordinates as the range of x and y coordinates, rather
  than the default values of (for type=mandel) -2.0/2.0/-1.5/1.5. When you
  specify four values (the usual case), this defines a rectangle: x-
  coordinates are mapped to the screen, left to right, from xmin to xmax,
  y-coordinates are mapped to the screen, bottom to top, from ymin to
  ymax. Six parameters can be used to describe any rotated or stretched
  parallelogram:  (xmin,ymax) are the coordinates used for the top-left
  corner of the screen, (xmax,ymin) for the bottom-right corner, and
  (x3rd,y3rd) for the bottom-left.

  CENTER-MAG=[Xctr/Yctr/Mag]
  This is an alternative way to enter corners as a center point and a
  magnification that is popular with some fractal programs and
  publications. Entering just "CENTER-MAG=" tells Fractint whether to use
  this form rather than corners when creating a batch file with the <B>
  command. The <TAB> status display shows the "corners" in both forms.
  Note that an aspect ratio of 1.3333 is assumed; if you have altered the
  zoom box proportions or rotated the zoom box, this form can no longer be
  used.

  PASSES=1|2|guess|btm
  Selects single-pass, dual-pass, solid-Guessing mode, or the Boundary
  Tracing algorithm.  The first two take the same total time to finish the
  display.  Solid-guessing is faster at the risk of errors for a few
  pixels.  Boundary tracing is sometimes faster, sometimes slower, and
  isn't correct for some fractal types at all (like the Newton fractals).

  FLOAT=yes
  Most fractal types have both a fast integer math and a floating point
  version. The faster, but possibly less accurate, integer version is the
  default. If you have a new 80486 or other fast machine with a math
  coprocessor, or if you are using the continuous potential option (which
  looks best with high bailout values not possible with our integer math
  implementation), you may prefer to use floating point. Just add
  "float=yes" to the command line to do so.

  MAXITER=nnn
  Reset the iteration maximum (the number of iterations at which the
  program gives up and says 'OK, this point seems to be part of the set in
  question and should be colored [insidecolor]') from the default 150.
  Values range from 10 to 32000 (super-high iteration limits like 30000
  are useful when using logarithmic palettes).

  INSIDE=nnn|bof60|bof61|attractor
  Set the color of the interior: for example, "inside=0" makes the M-set a
  stylish basic black. A setting of -1 makes inside=maxiter. Two more
  options reveal hidden structure inside the lake.  These are
  inside=bof61, and inside=bof62, named after the figures on pages 61 and

                     Fractint Version 15.0                     Page 60

  62 of "Beauty of Fractals". See Appendix for a brilliant explanation of
  what these do!

  OUTSIDE=nnn
  Set the color of the exterior: for example, "OUTSIDE=1" makes all points
  not INSIDE the fractal set to color 1 (blue). Note that defining an
  OUTSIDE color forces any image to be a two-color one: either a point is
  INSIDE the set, or it's OUTSIDE it.

  BAILOUT=nnn
  Over-rides the default bailout criterion for escape-time fractals. Can
  also be set from the parameters screen after selecting a fractal type.

  INITORBIT=pixel
  INITORBIT=nnn/nnn
  Allows control over the value used to begin each Mandelbrot-type orbit.
  "initorbit=pixel" is the default for most types; this command
  initializes the orbit to the complex number corresponding to the screen
  pixel. The command "initorbit=nnn/nnn" uses the entered value as the
  initializer. See the discussion of the MANDELLAMBDA type for more on
  this topic.

  POTENTIAL=maxcolor[/slope[/modulus[/16bit]]]
  Enables the "continuous potential" coloring mode for all fractal types
  except plasma clouds, IFS and IFS3D. The four arguments define the
  maximum color value, the slope of the potential curve, the modulus
  "bailout" value, and whether 16 bit values are to be calculated.
  Example: "POTENTIAL=240/2000/40/16bit". The Mandelbrot and Julia types
  ignore the modulus bailout value and use their own hardwired value of
  4.0 instead.  See chapter 6 on the continuous-potential algorithm for
  details.

  LOGMAP=yes|old|n
  Selects a compressed relationship between escape-time iterations and
  palette colors.  See "Logarithmic Palette" section for details.

  DISTEST=nnn
  Nonzero values enable the distance estimator method. Any nonzero value
  has the same effect in monochrome modes. Higher values result in more
  and narrower color bands in color modes; 1000 is a good value to try.

  DECOMP=2|4|8|16|32|64|128|256
  Invokes the corresponding decomposition coloring scheme.

  BIOMORPH=nnn
  Turn on biomorph option; set affected pixels to color nnn.

  INVERT=nn/nn/nn
  Turns on inversion. The parameters are radius of inversion, x-coordinate
  of center, and y-coordinate of center. -1 as the first parameter sets
  the radius to 1/6 the smaller screen dimension; no x/y parameters
  defaults to center of screen. The values are displayed with the <Tab>
  command.

                     Fractint Version 15.0                     Page 61

  FINATTRACT=no|yes
  Another option to show coloring inside some Julia "lakes" to show escape
  time to finite attractors. Works with lambda, magnet types, and possibly
  others.  See appendix for more information.

  FUNCTION=[fn1[/fn2[/fn3[/fn4]]]]
  Allows setting variable functions found in some fractal type formulae.
  Possible values are sin, cos, sinh, cosh, exp, log, and sqr.

  FORMULAFILE=[formulafilename]
  Specifies the default formula file for type=formula fractals (if not
  FRACTINT.FRM).  Handy if you want to generate one of these fractal types
  in batch mode.

  FORMULANAME=[formulaname]
  Specifies the default formula name for type=formula fractals (the
  default is no formula at all).  Required if you want to generate one of
  these fractal types in batch mode, as this is the only way to specify a
  formula name in that case.

  IFS=[filename]
  Use the IFS coded values in [filename] to generate Barnsley IFS fractal
  images. The default extension is .IFS. See chapter 2 for details.

  IFS3D=[filename]
  Use the IFS coded values in [filename] to generate Barnsley IFS3D
  fractals.

  LFILE=[lsystemfile]
  Specifies the default L-System file for type=lsystem fractals (if not
  FRACTINT.L).

  LNAME=[lsystemname]
  Specifies the default L-System name.  Required if you want to generate
  one of these fractal types in batch mode, as this is the only way to
  specify an L-System name in that case.

  PERIODICITY=no|show|nnn
  Allows control of periodicity checking.  "no" turns it off, "show" lets
  you see which pixels were painted the "inside" color due to being caught
  by periodicity.  Specifying a number causes a more conservative
  periodicity test (each increase of 1 divides the test tolerance by 2).
  Entering a negative number lets you turn on "show" with that number.
  Type lambdafn function=exp needs periodicity turned off to be accurate -
  - there may be other cases.

  SOUND=off|x|y|z
  We're all MUCH too busy to waste time with Fractint at work, and no
  doubt you are too, so "sound=off" is included only for use at home, to
  avoid waking the kids or your Significant Other, late at night. (By the
  way, didn't you tell yourself "just one more zoom on LambdaSine" an hour
  ago?) Suggestions for a "boss" hot-key will be cheerfully ignored, as
  this sucker is getting big enough without including a spreadsheet screen
  too. The "sound=x/y/x" options are for the "attractor" fractals, like
  the Lorenz fractals - they play with the sound on your PC speaker as

                     Fractint Version 15.0                     Page 62

  they are generating an image, based on the X or Y or Z co-ordinate they
  are displaying at the moment.  At the moment, "sound=x" (or y or z)
  really doesn't work very well when using an integer algorithm - try it
  with the floating-point toggle set, instead.

  HERTZ=nnn
  Adjusts the sound produced by the "sound=x/y/z" option.  Legal values
  are 200 through 10000.

  SAVENAME=[name]
  Set the filename to use when you <S>ave a screen. The default filename
  is FRACT001. The .GIF extension is optional (Example: SAVENAME=myfile)

  OVERWRITE=no|yes
  Sets the savename overwrite flag (default is 'no'). If 'yes', saved
  files will over-write existing files from previous sessions; otherwise
  the automatic incrementing of FRACTnnn.GIF will find the first unused
  filename.

  GIF87a=YES
  Backward-compatibility switch to force creation of GIF files in the
  GIF87a format.  As of version 14, Fractint now defaults to the new
  GIF89a format which permits storage of fractal information within the
  format. This switch is only needed if you wish to view Fractint images
  with a GIF decoder that cannot accept the newer format.

  BATCH=yes
  See "Batch Mode notes later in this chapter.

  SAVETIME=nnn
  Tells Fractint to automatically do a save every nnn minutes while a
  calculation is in progress.  This is mainly useful with long batches -
  see "Batch Mode".

  MAP=[filename]
  Reads in a replacement color map from [filename]. This map replaces the
  default video color map of your VGA or TARGA card. The file must be in
  the format described in chapter 6. The difference between this argument
  and an alternate map read in via <L> in color-command mode is that this
  one is permanent.

  CYCLELIMIT=nnn
  Sets the speed of color cycling. Technically, the number of DAC
  registers updated during a single vertical refresh cycle. Legal values
  are 1 - 256, default is 55.

  RSEED=nnnn
  The initial random-number "seed" for plasma clouds is taken from your
  PC's internal clock-timer. This argument forces a value (which you can
  see in the <Tab> display), and allows you to reproduce plasma clouds. A
  detailed discussion of why a TRULY random number may be impossible to
  define, let alone generate, will have to wait for "FRACTINT: The 3-MB
  Doc File."

                     Fractint Version 15.0                     Page 63

  BATCH=config
  Starts a quick batch-mode run that creates a default FRACTINT.CFG file
  from the full internal video table (FRACTINT.CFG is described in chapter
  7).

  SYMMETRY=xxx
  Forces symmetry to None, Xaxis, Yaxis, XYaxis, Origin, or Pi symmetry.
  Useful for debugging.

  ;
  Indicates the rest of the command line (or the rest of the individual
  line inside command files) is a comment.


 Video Parameters

  VIDEO=xxx
  Set the initial video mode (and bypass the informational screens). Handy
  for batch runs. (Example: VIDEO=F4 for IBM 16-color VGA.)
  (You can obtain the current VIDEO= values from the "Video Modes" help
  screens inside Fractint.  We don't duplicate them here only because they
  change so darned often!)

  ASKVIDEO=yes|no
  If "no," this eliminates the prompt asking you if a file to be restored
  is OK for your current video hardware.
  WARNING: every version of Fractint so far has had a bigger, better, but
  shuffled-around video table. Since calling for a mode your hardware
  doesn't support can leave your system in limbo, be careful about leaving
  this arguments in a command file to be used with future versions of
  Fractint, particularly for the super-VGA modes.

  ADAPTER=cga|ega|mcga|vga
  Skips the video autodetect logic, assumes the specified kind of adapter
  is present.  Use this only if you have trouble running up.

  TEXTSAFE=no
  If return from menu, prompt, or help to an image garbles the image, try
  specifying this.

  TEXTSAFE=yes
  To get rid of the irritating flicker on EGA/VGA during Fractint startup,
  try specifying this. Remove it if you find that images are scrambled
  when returning to them from the menu.

  EXITMODE=nn
  Sets the bios-supported videomode to use upon exit to the specified
  value.  nn is in hexadecimal.  The default is 3, which resets to 80x25
  color text mode on exit.

  TEXTCOLORS=mono
  Set text screen colors to simple black and white.

  TEXTCOLORS=aa/bb/cc/...
  Set text screen colors. Omit any value to use the default (e.g.

                     Fractint Version 15.0                     Page 64

  textcolors=////50 to set just the 5th value). Each value is a 2 digit
  hexadecimal value; 1st digit is background color (from 0 to 7), 2nd
  digit is foreground color (from 0 to F).
  Color values are:
      0 black     8 gray
      1 blue      9 light blue
      2 green     A light green
      3 cyan      B light cyan
      4 red       C light red
      5 magenta   D light magenta
      6 brown     E yellow
      7 white     F bright white
  27 colors can be specified, their meanings are as follows:
    heading:
      1  Fractint version info
      2  heading line development info (not used in released version)
    help:
      3  sub-heading
      4  main text
      5  instructions at bottom of screen
    menu, selection boxes, parameter input boxes:
      6  background around box and instructions at bottom
      7  low intensity information
      8  medium intensity information
      9  high intensity information (e.g. heading)
     10  current keyin field
     11  current choice in multiple choice list
     12  speed key prompt in multiple choice list
     13  speed key keyin in multiple choice list
    general (tab key display, IFS parameters, "thinking" display):
     14  high intensity information
     15  medium intensity information
     16  low intensity information
     17  current keyin field
    disk video:
     18  background around box
     19  high intensity information
     20  low intensity information
    diagnostic messages:
     21  error
     22  information
    credits screen:
     23  bottom lines
     24  high intensity divider line
     25  low intensity divider line
     26  primary authors
     27  contributing authors
  The default is
     textcolors=1F/1A/2E/70/28/78/17/1F/1E/2F/
                5F/07/0D/71/70/78/0F/70/0E/0F/
                4F/20/17/20/28/0F/07
  (In a real command file, all values must be on one line.)

                     Fractint Version 15.0                     Page 65

 Printer Parameters

  PRINTER=type[/resolution[/port#]]
  Defines your printer setup. The SSTOOLS.INI file is a REAL handy place
  to put this option, so that it's available whenever you have that
  sudden, irresistible urge for hard copy.
  Printer types:
    IB  IBM-compatible (default)
    EP  Epson-compatible
    HP  LaserJet
    CO  Star Micronics Color printer, supposedly Epson-color-compatible
    PA  Paintjet
    PS  PostScript
    PSL Postscript, landscape mode
  Resolution:
     In dots per inch. Currently available values are 60, 120, 240 for
    Epson/IBM; 75, 150, 300 for LaserJet; 90, 180 for Paintjet; 10 through
    600 for PostScript.
  Port:
    1, 2, 3 for LPT1-3; 11, 12, 13, 14 for COM1-4.  With PostScript, a
    negative port number can be used to redirect printing to a file.
    Default print-to-filename is FRACT001.PRN and is incremented after
    each print to file operation.

  COMPORT=port/baud/options
  Serial printer port initialization.
  Port=1,2,3,etc.
  Baud=115,150,300,600,1200,2400,4800,9600
  Options: 7,8 | 1,2 | e,n,o (any order).
  Example: comport=1/9600/n81 for COM1 set to 9600, no parity, 8 bits per
  character, 1 stop bit.

  TITLE=yes
  If specified, title information is added to printouts.

  Additional options for PostScript printers follow.

  PRINTFILE=filename
  Forces print-to-file (like negative port number) and specifies filename.

  EPSF=1|2|3
  Forces print-to-file and PostScript, but the default filename is
  FRACT001.EPS. The number determines how 'well-behaved' a .EPS file is. 1
  means by-the-book. 2 allows some EPS 'no-nos' like settransfer and
  setscreen - BUT includes code that should make the code still work
  without affecting the rest of the non-EPS document. 3 is a free-for-all.

  TRANSLATE=yes|-n|n
  Translate=yes prints the negative image of the fractal.
  Translate=n reduces the image to that many colors. A negative value
  causes a color reduction as well as a negative image.

  HALFTONE=frq/ang/sty
  Tells the PostScript printer how to define its halftone screen. The
  first value, frequency, defines the number of halftone lines per inch.

                     Fractint Version 15.0                     Page 66

  The second chooses the angle (in degrees) that the screen lies at. The
  third option chooses the halftone 'spot' style. Good default frequencies
  are between 60 and 80; Good default angles are 45 and 0; the default
  style is 0. If the halftone= option is not in SSTOOLS, Fractint will
  print using the printer's default halftone screen, which should have
  been already set to do a fine job on the printer. This option is
  presented here for the advanced PostScript owners and those who want to
  play around.
  Current halftone styles (no warranty on these!):
    0 - common circle screen (probably same as hardware default)
    2 - horizontal line screen
    4 - vertical line screen
    others - some have worked, some haven't. They SHOULD produce screens
    such as: boxes, crosses, rounded crosses, but aren't working as
    expected yet - explore if you like but don't expect wonders.


 3D Parameters

  3D=Yes
  Resets all 3d parameters to default values. If FILENAME= is given,
  forces the restore to be performed in 3D mode. Very handy when used with
  the 'batch=yes' option for batch-mode 3D images. If 3D=Yes follows the
  setting of any 3d parameters on the command line or in a command file,
  they will be reset to default values. (Note: the form
  "3D/=parm/parm/parm ..." for entering 3D parameters still works but will
  not be supported in the future. Use the variables below. Position-
  sensitive parameters are nasty and evil, especially when there are
  dozens of them!)

  The options below replace selected 3D defaults:
  SPHERE=yes                 Turns on spherical projection mode
  LONGITUDE=nn/nn            Longitude minimum and maximum
  LATITUDE=nn/nn             Latitude minimum and maximum
  RADIUS=nn                  Radius scale factor
  ROTATION=nn[/nn[/nn]]      Rotation about x,y, and z axes
  SCALEZYZ=nn/nn/nn          X,y,and z scale factors
  ROUGHNESS=nn               Same as z scale factor
  WATERLINE=nn               Colors nn and below will be "inside" color
  FILLTYPE=nn                3D filltype
  PERSPECTIVE=nn             Perspective distance
  XYSHIFT=nn/nn              Shift image in x and y directions with
                              perspective
  LIGHTSOURCE=nn/nn/nn       Coordinates for light-source vector
  SMOOTHING=nn               Smooths images in light-source fill modes
  TRANSPARENT=min/max        Defines a range of colors to be treated as
                              "transparent" when <O>verlaying 3D images.
  XYADJUST=nn/nn             This shifts the image in the x/y dir without
                              perspective
  STEREO=n                   Selects the type of stereo image creation
  INTEROCULAR=nn             Sets the interocular distance for stereo
  CONVERGE=nn                Determines the overall image separation
  CROP=nn/nn/nn/nn           Trims the edges off stereo pairs
  BRIGHT=nn/nn               Compensates funny glasses filter parameters

                     Fractint Version 15.0                     Page 67

  Below are new commands as of version 14 that support Marc Reinig's
  terrain features.

  RANDOMIZE=nnn  (0 - 100)
  This feature randomly varies the color of a pixel to near by colors.
  Useful to minimize map banding in 3d transformations. Usable with all
  FILLTYPES. 0 disables, max values is 7. Try 3 - 5.

  AMBIENT=nnn (0 - 100)
  Set the depth of the shadows when using full color and light source
  filltypes. "0" disables the function, higher values lower the contrast.

  FULLCOLOR=yes
  Valid with any light source FILLTYPE. Allows you to create a Targa-24
  file which uses the color of the image being transformed or the map you
  select and shades it as you would see it in real life. Well, its better
  than B&W. A good map file to use is topo

  HAZE=nnn (0 - 100)
  Gives more realistic terrains by setting the amount of haze for distant
  objects when using full color in light source FILLTYPES. Works only in
  the "y" direction currently, so don't use it with much y rotation. Try
  "rotation=85/0/0". 0 disables.

  LIGHTNAME=<filename>
  The name of the Targa-24 file to be created when using full color with
  light source. Default is light001.tga. If overwrite=no (the default),
  the file name will be incremented until an unused filename is found.
  Background in this file will be sky blue.

  To stay out of trouble, use the complete 3D list, even if you want to
  use what you think are the default values. It takes a little practice to
  learn what the default values really are. The best way to create a
  command file is to use the Batch command <B> on an image you like and
  then modify the resulting parameters.


 Setting Defaults (SSTOOLS.INI)

  If you are familiar with Microsoft's TOOLS.INI or WINDOWS.INI
  configuration files, the SSTOOLS.INI command file is used in the same
  way. In particular, you designate a section of SSTOOLS.INI as belonging
  to a particular program by beginning the section with a label in
  brackets. Fractint looks for the label [fractint], and ignores any lines
  it finds in the file belonging to any other label. If an SSTOOLS.INI
  file looks like this:

                     Fractint Version 15.0                     Page 68

  [fractint]
  sound=off                    ; (for home use only)
  printer=hp                   ; my printer is a LaserJet
  [startrek]
  Aye, captain, but I dinna think the engines can take it!
  [fractint]
  inside=0                     ; using "traditional" black

  Fractint will use only the second, third, and last lines of the file.

  (Why use a convention like that when Fractint is the only program you
  know of that uses an SSTOOLS.INI file?  Because there are other programs
  (such as Lee Crocker's PICLAB) that now use the same file, and people
  working on other, sister programs to Fractint are going to read that
  file. And just when you thought it was safe to download again..!)


 Batch Mode

  It IS possible, believe it or not, to become so jaded with the screen
  drawing process, so familiar with the types and options, that you just
  want to hit a key and do something else until the final images are safe
  on disk.  To do this, start Fractint with the BATCH=yes parameter added
  to the command line.  To create a batch file with the parameters
  required for a particular image you might:
   o Find an interesting area.  Note the parameters from the <Tab>
     display.  Then use an editor to write a batch file.
   o Find an interesting area.  Set all the parameters you'll want in the
     batch run.  Use the <B> command to store the parameters in
     FRABATCH.BAT.  Then use an editor to add the required batch mode
     parameters to the generated FRABATCH.BAT line.
  Another approach to batch mode calculations, using "FILENAME=" and
  resume, is described later.

  When modifying a command line generated by the <B> command, the only
  parameters you must add for a batch mode run are "BATCH=yes", and
  "VIDEO=xxx" to select a video mode.  You might want to also add
  "SAVENAME=[name]" to name the result as something other than the default
  FRACT001.GIF.  Watch out for the line exceeding the DOS limit of 120
  characters - if it does, use "fractint @filename" in your batch and put
  the parameters in another file "filename".

  "BATCH=yes" tells Fractint to run in batch mode -- that is, Fractint
  draws the image using whatever other parameters you specified, then acts
  as if you had hit <S> to save the image, then exits to DOS.

  "FILENAME=" can be used with "BATCH=yes" to resume calculation of an
  incomplete image.  For instance, you might interactively find an image
  you like; then select some slow options (a high resolution disk video
  mode, distance estimator method, high maxiter, or whatever);  start the
  calculation;  then interrupt immediately with a <S>ave.  Rename the save
  file (fract001.gif if it is the first in the session and you didn't name
  it with the <X> options or "savename=") to xxx.gif. Later you can run a
  batch file to finish the job:
      fractint batch=yes filename=xxx savename=xxx

                     Fractint Version 15.0                     Page 69


  "SAVETIME=nnn" is useful with long batch calculations, to store a
  checkpoint every nnn minutes.  If you start a many hour calculation with
  say "savetime=60", and a power failure occurs during the calculation,
  you'll have lost at most an hour of work on the image.  You can resume
  calculation from the save file as above.  Automatic saves triggered by
  SAVETIME do not increment the save file name. The same file is
  overwritten by each auto save until the image completes.  But note that
  Fractint does not directly over-write save files.  Instead, each save
  operation writes a temporary file FRACTINT.TMP, then deletes the prior
  save file, then renames FRACTINT.TMP to be the new save file.  This
  protects against power failures which occur during a save operation - if
  such a power failure occurs, the prior save file is intact and there's a
  harmless incomplete FRACTINT.TMP on your disk.

  If you want to spread a many-hour image over multiple bits of free
  machine time you could use a batch like:
      fractint batch=yes filename=xxx savename=xxx savetime=60
  While this batch is running, hit <S> (almost any key actually) to tell
  fractint to save what it has done so far and give your machine back.
  Kick off the batch again when you have another time slice for it.

  The SAVETIME= parameter, and batch resumes of partial calculations, only
  work with fractal types which can be resumed.  See "Interrupting and
  Resuming" for information about non-resumable types.

                     Fractint Version 15.0                     Page 70

 6. File Formats, Color Maps and All That


 Fractint and .GIF Files

  Since version 5.0, Fractint has had the <S>ave-to-disk command, which
  stores screen images in the extremely compact, flexible .GIF (Graphics
  Interchange Format) widely supported on Compuserve. Version 7.0 added
  the <R>estore-from-disk capability. Unfortunately, this created a
  problem. The then-current GIF87a specification did not offer a place to
  store the small amount of extra information that Fractint needs in order
  to implement the <R> feature -- i.e., the parameters that let you keep
  zooming, etc. so on as if the restored file had just been created in
  this session.

  Fractint got around this restriction in a non-standard manner, saving
  its application-specific information AFTER the official GIF terminator
  character. This trick worked with all of the popular GIF decoders that
  we had tested (although some of them required renaming the file to
  xxxx.GIF first).

  We did not claim that these files are true GIF files. For one thing,
  information after the GIF terminator has the potential to confuse the
  online GIF viewers used on Compuserve. For another, it is the opinion of
  some GIF developers that the addition of this extra information violates
  the GIF87a spec. That's why we used the default filetype .FRA instead.

  On August 1, 1990, Compuserve released an official upwardly-compatible
  extension of the GIF87a spec, called GIF89a.  This new spec allows the
  placement of application data within "extension blocks". Fractint
  version 14 supports the new spec. We have changed default savename
  extension from *.FRA to *.GIF.  Version 14 can still read *.FRA files
  generated by earlier versions.  If for some reason you wish to save
  files in the older GIF87a format, because, for example, your favorite
  GIF decoder has not yet been upgraded to GIF89a, just add the command-
  line parameter "GIF87a=yes".  Then any saved files will use the original
  GIF87a format without any application-specific information.

  An easy way to convert an older .FRA file into true .GIF format suitable
  for uploading is something like this at the DOS prompt:

  FRACTINT MYFILE.FRA SAVENAME=MYFILE.GIF BATCH=YES

  Fractint will load MYFILE.FRA, save it in true .GIF format as
  MYFILE.GIF, and return to DOS.

  There is one significant advantage to the new GIF89a format compared to
  the old GIF87a-based .FRA format for Fractint purposes:  the new .GIF
  files may be uploaded to the Compuserve graphics forums (such as
  Fractint's home forum, COMART) with fractal information intact.
  Therefore anyone downloading a Fractint image from Compuserve will also
  be downloading all the information needed to regenerate the image.

  GIF and "Graphics Interchange Format" are trademarks of Compuserve
  Incorporated, an H&R Block Company.

                     Fractint Version 15.0                     Page 71



 Continuous Potential

  Note: This option can only be used with 256 color modes.

  Fractint's images are usually calculated by the "level set" method,
  producing bands of color corresponding to regions where the calculation
  gives the same value. When viewed in 3D, most images other than plasma
  clouds are like terraced landscapes: most of the surface is either
  horizontal or vertical.

  To get the best results with the "illuminated" 3D fill options 5 and 6,
  there is an alternative approach that yields continuous changes in
  colors.

  Continuous potential is approximated by calculating

           potential =  log(modulus)/2^iterations

  where "modulus" is the orbit value (magnitude of the complex number)
  when the modulus bailout was exceeded, at the "iterations" iteration.
  Clear as mud, right?

  Fortunately, you don't have to understand all the details. However,
  there ARE a few points to understand. First, Fractint's criterion for
  halting a fractal calculation, the "modulus bailout value", is generally
  set to 4. Continuous potential is inaccurate at such a low value.

  The bad news is that the integer math which makes the "mandel" and
  "julia" types so fast imposes a hard-wired maximum value of 127. You can
  still make interesting images from those types, though, so don't avoid
  them. You will see "ridges" in the "hillsides." Some folks like the
  effect.

  The good news is that the other fractal types, particularly the
  (generally slower) floating point algorithms, have no such limitation.
  The even better news is that there is a floating-point algorithm for the
  "mandel" and "julia" types.  To force the use of a floating-point
  algorithm, use Fractint with the "FLOAT=YES" command-line toggle.  Only
  a few fractal types like plasma clouds, the Barnsley IFS/IFS3d types,
  and "test" are unaffected by this toggle.

  The parameters for continuous potential are:
      potential=maxcolor[/slope[/modulus[/16bit]]]
  These parameters are present on the <Y> options screen.

  "Maxcolor" is the color corresponding to zero potential, which plots as
  the TOP of the mountain. Generally this should be set to one less than
  the number of colors, i.e. usually 255. Remember that the last few
  colors of the default IBM VGA palette are BLACK, so you won't see what
  you are really getting unless you change to a different palette.

  "Slope" affects how rapidly the colors change -- the slope of the
  "mountains" created in 3D. If this is too low, the palette will not

                     Fractint Version 15.0                     Page 72

  cover all the potential values and large areas will be black. If it is
  too high, the range of colors in the picture will be much less than
  those available. There is no easy way to predict in advance what this
  value should be.

  "Modulus" is the bailout value used to determine when an orbit has
  "escaped". Larger values give more accurate and smoother potential. A
  value of 500 gives excellent results. As noted, this value must be <128
  for the integer fractal types (if you select a higher number, they will
  use 127).

  "16bit":  If you transform a continuous potential image to 3D, the
  illumination modes 5 and 6 will work fine, but the colors will look a
  bit granular. This is because even with 256 colors, the continuous
  potential is being truncated to integers. The "16bit" option can be used
  to add an extra 8 bits of goodness to each stored pixel, for a much
  smoother result when transforming to 3D.

  Fractint's visible behavior is unchanged when 16bit is enabled, except
  that solid guessing and boundary tracing are not used. But when you save
  an image generated with 16bit continuous potential:
   o The saved file is a fair bit larger.
   o Fractint names the file with a .POT extension instead of .GIF, if
     you didn't specify an extension in "savename".
   o The image can be used as input to a subsequent <3> command to get
     the promised smoother effect.
   o If you happen to view the saved image with a GIF viewer other than
     Fractint, you'll find that it is twice as wide as it is supposed to
     be. (Guess where the extra goodness was stored!) Though these files
     are structurally legal GIF files the double-width business made us
     think they should perhaps not be called GIF - hence the .POT
     filename extension.

  A 16bit (.POT) file can be converted to an ordinary 8 bit GIF by
  <R>estoring it, changing "16bit" to "no" on the <Y> options screen, and
  <S>aving.

  You might find with 16bit continuous potential that there's a long delay
  at the start of an image, and disk activity during calculation. Fractint
  uses its disk-video cache area to store the extra 8 bits per pixel - if
  there isn't sufficient memory available, the cache will page to disk.

  The following commands can be used to recreate the image that Mark
  Peterson first prototyped for us, and named "MtMand":

                  TYPE=mandel
                  CORNERS=-0.19920/-0.11/1.0/1.06707
                  INSIDE=255
                  MAXITER=255
                  POTENTIAL=255/2000/1000/16bit
                  PASSES=1
                  FLOAT=yes

                     Fractint Version 15.0                     Page 73

  Note that prior to version 15.0, Fractint:
   o Produced "16 bit TGA potfiles" This format is no longer generated,
     but you can still (for a release or two) use <R> and <3> with those
     files.
   o Assumed "inside=maxit" for continuous potential. It now uses the
     current "inside=" value - to recreate prior results you must be
     explicit about this parameter.


 Palette Maps

  If you have a VGA, Super-VGA, 8514/A, or TARGA video adapter, you can
  save and restore your color palette using special color-map files and
  either the command-line "map=" option, or the "L" and "S" commands in
  color-cycling and palette-editing modes.  These color-maps are ASCII
  files set up as a series of RGB triplet values (one triplet per line,
  encoded as the red, green, and blue [RGB] components of the color).

  Note that the color values are in GIF format - values go from 0 (low) to
  255 (high), so for a VGA adapter they get divided by 4 before being
  stuffed into the VGA's Video-DAC registers (so '6' and '7' end up
  referring to the same color value).

  The default filetype for color-map files is ".MAP".

  The distribution file contains sample .MAP files for you to examine and
  modify - DEFAULT.MAP (the VGA start-up values), ALTERN.MAP (the famous
  "Peterson-Vigneau Pseudo-Grey Scale"), GAMMA1.MAP and GAMMA2.MAP (Lee
  Crocker's response to ALTERN.MAP), LANDSCAP.MAP (Guruka Singh Khalsa's
  favorite color-map for plasma "landscapes"), TOPO.MAP (Monte Davis's
  contribution to full color terrain), and GRID.MAP (great for stereo
  surface grid images).

                     Fractint Version 15.0                     Page 74

 7. Hardware Support


  True to the spirit of public-domain programming, Fractint makes only a
  limited attempt to verify that your video adapter can run in the mode
  you specify, or even that an adapter is present, before writing to it.
  Hence the warning to check your "VIDEO=" argument before using a new
  version, in which the old key combo may now call an ultraviolet
  holographic mode.

  Fractint also assumes that every EGA adapter has a full 256K of memory
  (and can therefore display 640 x 350 x 16 colors), but does nothing to
  verify that fact before slinging pixels.


 Notes on Video Modes, "Standard" and Otherwise

  Fractint uses a video adapter table in the "C" program for everything it
  needs to know about any particular adapter/mode combination. This table
  can contain information for up to 98 adapter/mode combinations, and is
  automatically tied to 84 keys (F2-F10, their Control/ Shift/Alt
  variants, and many Alt-x keypad combos) when the program is running.
  The table entries, and the function keys they are tied to, are displayed
  as part of the help screens and in the video mode selection list.

  This table makes adding support for various third-party video cards and
  their modes much easier, at least for the ones that pretend to be a
  standard adapter with more dots and/or colors. There is even a special
  "roll-your-own" video mode (mode 19) enabling those of you with "C"
  compilers and a copy of the Fractint source to generate video modes
  supporting whatever adapter you may have. You can customize the table
  using the external configuration file FRACTINT.CFG, described below.

  The table as currently distributed begins with nine standard and several
  non-standard IBM video modes that have been exercised successfully with
  a PS/2 model 80. These entries, coupled with the descriptive comments in
  the table definition and the information supplied (or that should have
  been supplied!) with your video adapter, should be all you need to add
  your own entries.

  320 x 400 x 256 and 360 x 480 x 256 VGA MODES

  The IBM VGA adapter is a highly programmable device, and can be set up
  to display many video-mode combinations beyond those "officially"
  supported by the IBM BIOS. These video modes are perfectly legal, but
  temporarily reprogram the adapter (IBM or fully register-compatible) in
  a non-standard manner that the BIOS does not recognize. Because of this,
  the program cannot send any text to the screen while it is in one of
  these modes (the BIOS would garbage it). An internal flag inhibits all
  text output while the screen is in one of these video modes. Fractint's
  <F1> (help) and <Tab> commands still work, because they temporarily
  switch the screen to an alternate video mode.

                     Fractint Version 15.0                     Page 75

  8514/A MODES

  The IBM 8514/A modes use IBM's software interface, and require the pre-
  loading of IBM's HDIDLOAD TSR utility. There are two sets of 8514/A
  modes: full sets (640x480, 1024x768) which cover the entire screen and
  do NOT have a border color (so that you cannot tell when you are
  "paused" in a color-cycling mode), and partial sets (632x474, 1016x762)
  with small border areas which do turn white when you are paused in
  color-cycling mode. Also, while these modes are declared to be 256-
  color, if you do not have your 8514/A adapter loaded with its full
  complement of memory you will actually be in 16-color mode. Finally,
  because IBM's interface does not handle drawing single pixels very well
  (we have to draw a 1x1 pixel "box"), generating the zoom box is
  excruciatingly slow. Still, it works!

  SUPER-EGA AND SUPER-VGA MODES

  After the IBM and quasi-pseudo-demi-IBM modes, the table contains an
  ever-increasing number of entries for other adapters. Almost all of
  these entries have been added because someone like you sent us spec
  sheets, or modified Fractint to support them and then informed us about
  it.  With version 12.0, we've added both John Bridges' SuperVGA
  Autodetecting logic *and* VESA adapter detection, so that many of the
  brand-specific SuperVGA modes have been collapsed into a single function
  key.  There is now exactly one function key for SuperVGA 640x480x256
  mode, for instance.

  TARGA MODES

  TARGA support for Fractint is provided courtesy of Joe McLain. Be aware
  that there are a LOT of possible TARGA configurations, and a LOT of
  opportunities for a TARGA board and a VGA or EGA board to interfere with
  each other, and we may not have all of them smoothed away yet.  Also,
  the TARGA boards have an entirely different color-map scheme than the
  VGA cards, and at the moment they cannot be run through the color-
  cycling menu. The "MAP=" argument (chapter 5), however, works with both
  TARGA and VGA boards and enables you to redefine the default color maps
  with either board.

  "DISK-VIDEO" MODES

  These "video modes" do not involve a video adapter at all. They use (in
  order or preference) your expanded memory, your extended memory, or your
  disk drive (as file FRACTINT.DSK) to store the fractal image. These
  modes are useful for creating images beyond the capacity of your video
  adapter, right up to the current internal limit of 2048 x 2048 x 256,
  and for background processing under multi-tasking DOS managers.

  While you are in a disk-video mode, your screen will display text
  information indicating whether memory or your disk drive is being used,
  and what portion of the "screen" is being read from or written to.  A
  "Cache size" figure is also displayed. 24K is the maximum cache size.
  If you see a number less than this, it means that you don't have a lot
  of memory free, and that performance will be less than optimum.  With a
  very low cache size such as 4 or 6k, performance gets considerably worse

                     Fractint Version 15.0                     Page 76

  in cases using solid guessing, boundary tracing, plasma, or anything
  else which paints the screen non-linearly.  If you have this problem,
  all we can suggest is having less TSR utilities loaded before starting
  Fractint, or changing in your config.sys file, such as reducing a very
  high BUFFERS value.

  The zoom box is disabled during disk-video modes (you couldn't see where
  it is anyway).  So is the orbit display feature.

  When using real disk for your disk-video, Fractint will not generate
  some "attractor" types (e.g. lorenz) nor "IFS" images.  These would kill
  your disk drive.  Boundary tracing is allowed - it may give your drive a
  bit of a workout, but is generally tolerable.

  When using a real disk, and you are not directing the file to a RAM
  disk, and you aren't using a disk caching program on your machine,
  specifying BUFFERS=10 (or more) in your config.sys file is best for
  performance.  BUFFERS=10,2 or even BUFFERS=10,4 is also good.  It is
  also best to keep your disk relatively "compressed" (or "defragmented")
  if you have a utility to do this.

  In order to use extended memory, you must have HIMEM.SYS or an
  equivalent that supports the XMS 2.0 standard or higher.  Also, you
  can't have a VDISK installed in extended memory.  Himem.sys is
  distributed with Microsoft Windows 286/386 and 3.0.  If you have
  problems using the extended memory, try rebooting with just himem.sys
  loaded and see if that clears up the problem.

  If you are running background disk-video fractals under Windows 3, and
  you don't have a lot of real memory (over 2Mb), you might find it best
  to force Fractint to use real disk for disk-video modes.  (Force this by
  using a .pif file with extended memory and expanded memory set to zero.)
  Try this if your disk goes crazy when generating background images,
  which are supposedly using extended or expanded memory.  This problem
  can occur because, to multi-task, sometimes Windows must page an
  application's expanded or extended memory to disk, in big chunks.
  Fractint's own cached disk access may be faster in such cases.

  "TWEAKED" VGA MODES

  Fractint contains code that sets up the IBM (or any truly register-
  compatible) VGA adapter for several extended modes such as 704x528,
  736x552, 768x576, and 800x600. It does this by programming the VGA
  controller to use the fastest dot-clock on the IBM adapter (28.322 MHz),
  throwing more pixels, and reducing the refresh rate to make up for it.

  These modes push many monitors beyond their rated specs, in terms of
  both resolution and refresh rate. Signs that your monitor is having
  problems with a particular "tweaked" mode include:
   o vertical or horizontal overscan (displaying dots beyond the edges of
     your visible CRT area)
   o flickering (caused by a too-slow refresh rate)
   o vertical roll or total garbage on the screen (your monitor simply
     can't keep up, or is attempting to "force" the image into a pre-set
     mode that doesn't fit).

                     Fractint Version 15.0                     Page 77


  We have successfully tested the modes up to 768x576 on an IBM PS/2 Model
  80 connected to IBM 8513, IBM 8514, NEC Multisync II, and Zenith 1490
  monitors (all of which exhibit some overscan and flicker at the highest
  rates), and have tested 800x600 mode on the NEC Multisync II (although
  it took some twiddling of the vertical-size control).


 FRACTINT.CFG (Customized Video Mode List)

  If you have a favorite adapter/video mode that you would like to add to
  Fractint... if you want to remove table entries that do not apply to
  your system... if you're bothered that your favorite mode requires the
  <Alt><Left-Shift><Swizzlestick> key combination... or if you are using a
  non-enhanced keyboard so that you can't USE that combination ... relief
  is here, and without even learning "C"!

  Fractint will create an external, editable video configuration file
  called FRACTINT.CFG, and from then on will use that instead of its
  internal table as long as it can locate it somewhere along the DOS path.
  Enter FRACTINT BATCH=CONFIG, and you will get a default file with an
  entry for every one of the internal video table entries, and you can go
  to work on it with a text editor.

  Any line in the file that begins with a tab or a space (or is empty) is
  treated as a comment. The rest of the lines must consist of ten fields
  separated by commas. The ten fields are defined as:

  1. The name of the adapter/video mode (25 chars max, no leading blanks).
  The adapter is set up for that mode via INT 10H, with:
  2. AX = this,
  3. BX = this,
  4. CX = this, and
  5. DX = this (hey, having all these registers wasn't OUR idea!)
  6. An encoded value describing how to write to your video memory in that
  mode. Currently available codes are:
    1) Use the BIOS (INT 10H, AH=12/13, AL=color) (last resort - SLOW!)
    2) Pretend it's a (perhaps super-res) EGA/VGA
    3) Pretend it's an MCGA
    4) SuperVGA 256-Color mode using the Tseng Labs chipset
    5) SuperVGA 256-Color mode using the Paradise chipset
    6) SuperVGA 256-Color mode using the Video-7 chipset
    7) Non-Standard IBM VGA 360 x 480 x 256-Color mode
    8) SuperVGA 1024x768x16 mode for the Everex chipset
    9) TARGA video modes
   10) HERCULES video mode
   11) Non-Video, i.e. "disk-video"
   12) 8514/A video modes
   13) CGA 320x200x4-color and 640x200x2-color modes
   14) Reserved for Tandy 1000 video modes
   15) SuperVGA 256-Color mode using the Trident chipset
   16) SuperVGA 256-Color mode using the Chips & Tech chipset
   17) SuperVGA 256-Color mode using the ATI VGA Wonder chipset
   18) SuperVGA 256-Color mode using the EVEREX chipset
   19) Roll-your-own video mode (as you've defined it in YOURVID.C)

                     Fractint Version 15.0                     Page 78

   20) SuperVGA 1024x768x16 mode for the ATI VGA Wonder chipset
   21) SuperVGA 1024x768x16 mode for the Tseng Labs chipset
   22) SuperVGA 1024x768x16 mode for the Trident chipset
   23) SuperVGA 1024x768x16 mode for the Video 7 chipset
   24) SuperVGA 1024x768x16 mode for the Paradise chipset
   25) SuperVGA 1024x768x16 mode for the Chips & Tech chipset
   26) SuperVGA 1024x768x16 mode for the Everex Chipset
   27) SuperVGA Auto-Detect mode (we poke around looking for your adapter)
   28) VESA modes

  7. The number of pixels across the screen (X - 160 to 2048)
  8. The number of pixels down the screen (Y - 160 to 2048)
  9. The number of available colors (2, 4, 16, or 256)
  10. A comment describing this mode (25 chars max, leading blanks are OK)

  NOTE that the AX, BX, CX, and DX fields are generated (and read back)
  using hexadecimal notation (fifteen ==> 'f', sixteen ==> '10'), because
  that's the way most adapter documentation describes it. The other fields
  use standard decimal notation.

  If you look closely at the default entries, you will notice that the IBM
  VGA entries labeled "tweaked" and "non standard" have entries in the
  table with AX = BX = CX = 0, and DX = some other number. Those are
  special flags that we used to tell the program to custom-program the VGA
  adapter, and are NOT undocumented BIOS calls. Maybe they should be, but
  they aren't.

  If you have a fancy adapter and a new video mode that works on it, and
  it is not currently supported, PLEASE GET THAT INFORMATION TO US!  We
  will add the video mode to the list on our next release, and give you
  credit for it. Which brings up another point: If you can confirm that a
  particular video adapter/mode works (or that it doesn't), and the
  program says it is UNTESTED, please get that information to us also.
  Thanks in advance!

                     Fractint Version 15.0                     Page 79

 8. Common Problems

  Of course, Fractint would never stoop to having a "common" problem.
  These notes describe some, ahem, "special situations" which come up
  occasionally and which even we haven't the gall to label as "features".

  Hang during startup:
    There might be a problem with Fractint's video detection logic and
    your particular video adapter.  Try running with "fractint
    adapter=xxx" where xxx is cga, ega, mcga, or vga.  Note that when
    Fractint is started this way, you may not be able to use the highest
    resolution modes supported by your adapter.  If this solves the
    problem, create an SSTOOLS.INI file with the "adapter=xxx" command in
    it so that the fix will apply to every run.
    Another possible cause:  If you install the latest Fractint in say
    directory "newfrac", then run it from another directory with the
    command "\newfrac\fractint", *and* you have an older version of
    fractint.exe somewhere in your DOS PATH, a silent hang is all you'll
    get.  See the notes under "Cannot find FRACTINT.EXE message" for the
    reason.

  Scrambled image when returning from a text mode display:
    If an image which has been partly or completely generated gets partly
    destroyed when you return to it from the menu, help, or the
    information display, try starting with "fractint textsafe=no".  If
    this cures the problem, create an SSTOOLS.INI file with the
    "textsafe=no" command so that the fix will apply to every run.
    There are a number of known cases where "textsafe=no" will not cure
    the problem.  This happens mostly with SVGA boards in higher
    resolution modes.  Sorry, but we don't have a fix for this yet - we're
    working on it, perhaps for a near-future version 15.1.  The problem
    appears to be bios-related; unfortunately the fix will probably be an
    option which will slow down switches to and from text mode quite a
    bit.
    For now, if you have this problem and "textsafe=no" doesn't fix it ,
    all we can suggest is avoiding invoking the menu, help, and <tab>
    displays while generating or viewing an image in the video modes which
    have this problem.

  Coarse monochrome text:
    You may find that the menu, help screens, and fractal information
    screen sometimes display in color, sometimes in coarse monochrome
    characters.  The monochrome text occurs if you specify "textsafe=no",
    or if Fractint finds during initialization that your video adapter
    does not behave in a standard way.  In these cases you may prefer to
    run with the "textcolors=mono" command for a more consistent
    appearance in Fractint's text screens.

  Other video problems:
    We've had one case where a video driver for Windows does not work
    properly with Fractint.  If running under Windows, DesqView, or some
    other layered environment, try running Fractint directly from DOS to
    see if that avoids the problem.
    We've also had one case of a problem co-existing with "386 to the
    Max".

                     Fractint Version 15.0                     Page 80

    Also, see the "Hardware Support" section of the manual for information
    about enhanced video modes - Fractint makes only limited attempts to
    verify that a video mode you request is actually supported by your
    adapter.

  Insufficient memory:
    Fractint requires a fair bit of memory to run.  Most machines with at
    least 640k (ok sticklers, make that "PC-compatible" machines) will
    have no problem.  Machines with 512k and machines with many TSR
    utilities and/or a LAN interface may have problems.  Some Fractint
    features allocate memory when required during a run.  If you get a
    message about insufficient memory, or suspect that some problem is due
    to a memory shortage, you could try commenting out some TSR utilities
    in your AUTOEXEC.BAT file, some non-critical drivers in your
    CONFIG.SYS file, or reducing the BUFFERS parameter in your CONFIG.SYS.

  "Cannot find FRACTINT.EXE" message:
    Fractint is an overlayed program - some parts of it are brought from
    disk into memory only when used.  The overlay manager needs to know
    where to find the program.  It must be named FRACTINT.EXE (which it is
    unless somebody renamed it), and you should either be in the directory
    containing it when you start Fractint, or that directory should be in
    your DOS PATH.

  Disk video mode performance:
    This won't be blindingly fast at the best of times, but there are
    things which can slow it down and can be tuned.  See "Disk Video
    Modes" in "Hardware Support" for details.

                     Fractint Version 15.0                     Page 81

 9. Fractals and the PC


 A Little History


  Before Mandelbrot

  Like new forms of life, new branches of mathematics and science don't
  appear from nowhere. The ideas of fractal geometry can be traced to the
  late nineteenth century, when mathematicians created shapes -- sets of
  points -- that seemed to have no counterpart in nature.  By a wonderful
  irony, the "abstract" mathematics descended from that work has now
  turned out to be MORE appropriate than any other for describing many
  natural shapes and processes.

  Perhaps we shouldn't be surprised.  The Greek geometers worked out the
  mathematics of the conic sections for its formal beauty; it was two
  thousand years before Copernicus and Brahe, Kepler and Newton overcame
  the preconception that all heavenly motions must be circular, and found
  the ellipse, parabola, and hyperbola in the paths of planets, comets,
  and projectiles.

  In the 17th century Newton and Leibniz created calculus, with its
  techniques for "differentiating" or finding the derivative of functions
  -- in geometric terms, finding the tangent of a curve at any given
  point.  True, some functions were discontinuous, with no tangent at a
  gap or an isolated point. Some had singularities: abrupt changes in
  direction at which the idea of a tangent becomes meaningless. But these
  were seen as exceptional, and attention was focused on the "well-
  behaved" functions that worked well in modeling nature.

  Beginning in the early 1870s, though, a 50-year crisis transformed
  mathematical thinking. Weierstrass described a function that was
  continuous but nondifferentiable -- no tangent could be described at any
  point. Cantor showed how a simple, repeated procedure could turn a line
  into a dust of scattered points, and Peano generated a convoluted curve
  that eventually touches every point on a plane. These shapes seemed to
  fall "between" the usual categories of one-dimensional lines, two-
  dimensional planes and three-dimensional volumes. Most still saw them as
  "pathological" cases, but here and there they began to find
  applications.

  In other areas of mathematics, too, strange shapes began to crop up.
  Poincare attempted to analyze the stability of the solar system in the
  1880s and found that the many-body dynamical problem resisted
  traditional methods. Instead, he developed a qualitative approach, a
  "state space" in which each point represented a different planetary
  orbit, and studied what we would now call the topology -- the
  "connectedness" -- of whole families of orbits. This approach revealed
  that while many initial motions quickly settled into the familiar
  curves, there were also strange, "chaotic" orbits that never became
  periodic and predictable.

                     Fractint Version 15.0                     Page 82

  Other investigators trying to understand fluctuating, "noisy" phenomena
  -- the flooding of the Nile, price series in economics, the jiggling of
  molecules in Brownian motion in fluids -- found that traditional models
  could not match the data. They had to introduce apparently arbitrary
  scaling features, with spikes in the data becoming rarer as they grew
  larger, but never disappearing entirely.

  For many years these developments seemed unrelated, but there were
  tantalizing hints of a common thread. Like the pure mathematicians'
  curves and the chaotic orbital motions, the graphs of irregular time
  series often had the property of self-similarity: a magnified small
  section looked very similar to a large one over a wide range of scales.


  Who Is This Guy, Anyway?

  While many pure and applied mathematicians advanced these trends, it is
  Benoit Mandelbrot above all who saw what they had in common and pulled
  the threads together into the new discipline.

  He was born in Warsaw in 1924, and moved to France in 1935. In a time
  when French mathematical training was strongly analytic, he visualized
  problems whenever possible, so that he could attack them in geometric
  terms.  He attended the Ecole Polytechnique, then Caltech, where he
  encountered the tangled motions of fluid turbulence.

  In 1958 he joined IBM, where he began a mathematical analysis of
  electronic "noise" -- and began to perceive a structure in it, a
  hierarchy of fluctuations of all sizes, that could not be explained by
  exiting statistical methods. Through the years that followed, one
  seemingly unrelated problem after another was drawn into the growing
  body of ideas he would come to call fractal geometry.

  As computers gained more graphic capabilities, the skills of his mind's
  eye were reinforced by visualization on display screens and plotters.
  Again and again, fractal models produced results -- series of flood
  heights, or cotton prices -- that experts said looked like "the real
  thing."

  Visualization was extended to the physical world as well. In a
  provocative essay titled "How Long Is the Coast of Britain?" Mandelbrot
  noted that the answer depends on the scale at which one measures: it
  grows longer and longer as one takes into account every bay and inlet,
  every stone, every grain of sand. And he codified the "self-similarity"
  characteristic of many fractal shapes -- the reappearance of
  geometrically similar features at all scales.

  First in isolated papers and lectures, then in two editions of his
  seminal book, he argued that many of science's traditional mathematical
  models are ill-suited to natural forms and processes: in fact, that many
  of the "pathological" shapes mathematicians had discovered generations
  before are useful approximations of tree bark and lung tissue, clouds
  and galaxies.

                     Fractint Version 15.0                     Page 83

  Mandelbrot was named an IBM Fellow in 1974, and continues to work at the
  IBM Watson Research Center. He has also been a visiting professor and
  guest lecturer at many universities.


 A Little Code


  Periodicity Logic

  The "Mandelbrot Lake" in the center of the M-set images is the
  traditional bane of plotting programs. It sucks up the most computer
  time because it always reaches the iteration limit -- and yet the most
  interesting areas are invariably right at the edge the lake.

  Thanks to Mark Peterson for pointing out (well, he more like beat us
  over the head until we paid attention) that the iteration values in the
  middle of Mandelbrot Lake tend to decay to periodic loops (i.e., Z(n+m)
  == Z(n), a fact that is pointed out on pages 58-61 of "The Beauty of
  Fractals"). An intelligent program (like the one he wrote) would check
  for this periodicity once in a while, recognize that iterations caught
  in a loop are going to max out, and bail out early.

  For speed purposes, the current version of the program turns this
  checking algorithm on only if the last pixel generated was in the lake.
  (The checking itself takes a small amount of time, and the pixels on the
  very edge of the lake tend to decay to periodic loops very slowly, so
  this compromise turned out to be the fastest generic answer).

  Try a full M-set plot with a 1000-iteration maximum with any other
  program, and then try it on this one for a pretty dramatic proof of the
  value of periodicity checking.

  You can get a visual display of the periodicity effects if you press
  <O>rbits while plotting. This toggles display of the intermediate
  iterations during the generation process.  It also gives you an idea of
  how much work your poor little PC is going through for you!  If you use
  this toggle, it's best to disable solid-guessing first using <1> or <2>
  because in its second pass, solid-guessing bypasses many of the pixel
  calculations precisely where the orbits are most interesting.

  Mark was also responsible for pointing out that 16-bit integer math was
  good enough for the first few levels of M/J images, where the round-off
  errors stay well within the area covered by a single pixel. Fractint now
  uses 16-bit math where applicable, which makes a big difference on non-
  32-bit PCs.

                     Fractint Version 15.0                     Page 84

  Limitations of Integer Math (And How We Cope)

  By default, Fractint uses 16-bit and/or 32-bit integer math to generate
  nearly all its fractal types. The advantage of integer math is speed:
  this is by far the fastest such plotter that we have ever seen on any
  PC. The disadvantage is an accuracy limit. Integer math represents
  numbers like 1.00 as 32-bit integers of the form [1.00 * (2^29)]
  (approximately 500,000,000 digits!) for the Mandelbrot and Julia sets.
  Other integer fractal types use a bitshift of 24 rather than 29, so 1.0
  is stored internally as [1.00 * (2^*24)]. This yields accuracy of better
  than 8 significant digits, and works fine... until the initial values of
  the calculations on consecutive pixels differ only in the ninth decimal
  place.

  At that point, if Fractint has a floating-point algorithm handy for that
  particular fractal type (and virtually all of the fractal types have one
  these days), it will silently switch over to the floating-point
  algorithm and keep right on going.  Fair warning - if you don't have an
  FPU, the effect is that of a rocket sled hitting a wall of jello, and
  even if you do, the slowdown is noticeable.

  If it has no floating-point algorithm, Fractint does the best it can: it
  switches to its minimal drawing mode, with adjacent pixels having
  initial values differing by 1 (really 0.000000002).  Attempts to zoom
  further may result in moving the image around a bit, but won't actually
  zoom.  If you are stuck with an integer algorithm, you can reach minimal
  mode with your fifth consecutive "maximum zoom", each of which covers
  about 0.25% of the previous screen. By then your full-screen image is an
  area less than 1/(10^13)th [~0.0000000000001] the area of the initial
  screen.  (If your image is rotated or stretched very slightly, you can
  run into the wall of jello as early as the fourth consecutive maximum
  zoom.  Rotating or stretching by larger amounts has less impact on how
  soon you run into it.)

  Think of it this way: at minimal drawing mode, your VGA display would
  have to have a surface area of over one million square miles just to be
  able to display the entire M-set using the integer algorithms.  Using
  the floating-point algorithms, your display would have to be big enough
  to fit the entire solar system out to the orbit of Saturn inside it.  So
  there's a considerable saving on hardware, electricity and desk space
  involved here.  Also, you don't have to take out asteroid insurance.

  32 bit integers also limit the largest number which can be stored.  This
  doesn't matter much since numbers outside the supported range (which is
  between -4 and +4) produce a boring single color. If you try to zoom-out
  to reduce the entire Mandelbrot set to a featureless speck, or to
  squeeze it to a pancake, you'll find you can't do so in integer math
  mode.

                     Fractint Version 15.0                     Page 85

  The Fractint "Fractal Engine" Architecture

  Several of the authors would never ADMIT this, but Fractint has evolved
  a powerful and flexible architecture that makes adding new fractals very
  easy. (They would never admit this because they pride themselves on
  being the sort that mindlessly but happily hacks away at code and "sees
  if it works and doesn't hang the machine".)

  Many fractal calculations work by taking a rectangle in the complex
  plane, and, point by point, calculating a color corresponding to that
  point.  Furthermore, the color calculation is often done by iterating a
  function over and over until some bailout condition is met.

  In implementing such a scheme, there are three fractal-specific
  calculations that take place within a framework that is pretty much the
  same for them all.  Rather than copy the same code over and over, we
  created a standard fractal engine that calls three functions that may be
  bolted in temporarily to the engine.  The "bolting in" process uses the
  C language mechanism of variable function pointers.

  These three functions are:

     1) a setup function that is run once per image, to do any required
     initialization of variables,

     2) a once-per-pixel function that does whatever initialization has
     to be done to calculate a color for one pixel, and

     3) a once-per-orbit-iteration function, which is the fundamental
     fractal algorithm that is repeatedly iterated in the fractal
     calculation.

  The common framework that calls these functions can contain all sorts of
  speedups, tricks, and options that the fractal implementor need not
  worry about.  All that is necessary is to write the three functions in
  the correct way, and BINGO! - all options automatically apply. What
  makes it even easier is that usually one can re-use functions 1) and 2)
  written for other fractals, and therefore only need to write function
  3).

  Then it occurred to us that there might be more than one sort of fractal
  engine, so we even allowed THAT to be bolted in. And we created a data
  structure for each fractal that includes pointers to these four
  functions, various prompts, a default region of the complex plane, and
  various miscellaneous bits of information that allow toggling between
  Julia and Mandelbrot or toggling between the various kinds of math used
  in implementation.

  That sounds pretty flexible, but there is one drawback - you have to be
  a C programmer and have a C compiler to make use of it! So we took it a
  step further, and designed a built-in high level compiler, so that you
  can enter the formulas for the various functions in a formula file in a
  straightforward algebra-like language, and Fractint will compile them
  and bolt them in for you!

                     Fractint Version 15.0                     Page 86

  There is a terrible down side to this flexibility.  Fractint users
  everywhere are going berserk. Fractal-inventing creativity is running
  rampant. Proposals for new fractal types are clogging the mail and the
  telephones.

  All we can say is that non-productivity software has never been so
  potent, and we're sorry, it's our fault!

  Fractint was compiled using Microsoft C 5.1 and Microsoft Assembler 5.1
  using the "Medium" model. Note that the assembler code uses the "C"
  model option added to version 5.1, and must be assembled with the /MX or
  /ML switch to link with the "C" code. Because it has become too large to
  distribute comfortably as a single compressed file, and because many
  downloaders have no intention of ever modifying it, it is now
  distributed as two files: one containing FRACTINT.EXE, auxiliary files
  and this document, and another containing complete source code
  (including a .MAK file and MAKEFRAC.BAT).

                     Fractint Version 15.0                     Page 87

 Appendix A  Mathematics of the Fractal Types


  For functions below, "pixel" is the complex number corresponding to the
  current pixel. "Fn" can be replace by sin, cos, sinh, cosh, exp, log or
  sqr. "^" is the exponential operator, z(n) denotes the nth complex orbit
  value in the sequence z(0), z(1), ..., z(n), z(n+1),...

  Fractal Type(s)             Formula(s) used
  -----------------------     -------------------------------------------
  Mandel, Julia               z(n+1) = z(n)^2 + C
  Newton, Newtbasin           (roots of) z^n - 1, where n is an integer
  ComplexNewton, ComplexBasin (roots of) z^a - b, where a,b are complex
  plasma                      (see the Plasma section for details)
  Mandelfn, Lambdafn           z(n+1) = Lambda*fn(z(n))+C (function=sin,
                                cos, sinh, cosh, exp, log, or sqr)
  BarnsleyM1, BarnsleyJ1      z(n+1) = (z(n)-1) * C if Real(z) >= 0
                               else    (z(n)+1) * modulus(C)/C
  BarnsleyM2, BarnsleyJ2      z(n+1) = (z(n)-1) * C if Real(z(n))*Imag(C)
                                       +Real(C)*Imag(z(n)) >= 0
                               else    (z(n)+1) * C
  BarnsleyM3, BarnsleyJ3      z(n+1) = (Real(z(n))^2 - Imag(z(n))^2 - 1)
                                      + i * (2*Real(z((n)) * Imag(z((n)))
                                        if Real(z(n) > 0
                               else    (Real(z(n))^2 - Imag(z(n))^2 - 1
                                      + lambda * Real(z(n))
                                      + i * (2 * Real(z((n)) * Imag(z((n))
                                             + lambda * Real(z(n))
  Sierpinski                  z(n+1) = (2x, 2y - 1) if y > .5
                               else    (2x - 1, 2y) if x > .5
                               else    (2X, 2y)
  MandelLambda, Lambda        z(n+1) = (C) * (z(n)^2) + C
  MarksMandel, MarksJulia     z(n+1) = (C^(Period-1)) * (z(n)^2) + C
                              ("Period" is a parameter)
  Cmplxmarksmand,Cmplxmarksjul Same as MarksMandel and MarksJulia except
                              period parameter is complex rather than real
  Unity                       (see the Unity section for details)
  ifs, ifs3D                  (see the IFS section for details)
  Mandel4, Julia4             z(n+1) = z(n)^4 + C
  Test                        (as distributed, as simple Mandelbrot
  fractal)
  Manfn+zsqrd, Julfn+zsqrd    z(n+1) =  fn(z(n)) + z(n)^2 + C
  Manzpower, Julzpower        z(n+1) = z(n)^M + C (M is a parameter)
  Mandel4/Julia4              Special case of manzpower/julzpower (M=4)
  Manzzpwr, Julzzpwr          z(n+1) = z(n)^z(n) + z(n)^M + C
  Manfn+exp, Julfn+exp        z(n+1) = fn(z(n)) + e^(z(n)) + C
  popcorn                     z(n+1) = x(n+1) + i * y(n+1), where
                              x(n+1) = x(n) - 0.05*sin(y(n)) + tan(3*y(n))
                              y(n+1) = y(n) - 0.05*sin(x(n)) + tan(3*x(n))
  popcornjul                  Julia calculation from the popcorn formula.
  Bifurcation                 (see the Bifurcation section for details)
  Bif+sinpi
  Bif=sinpi
  Biflambda

                     Fractint Version 15.0                     Page 88

  Lorenz, Lorenz3d            Lorenz Attractor - orbits of differential
                              equation:
                              dx/dt = -a*x + a*y
                              dy/dt =  b*x - y   -z*x
                              dz/dt = -c*z + x*y
                              Solution by 1st order Taylor series:
                              xnew = x + (-a*x*dt) + (a*y*dt)
                              ynew = y + (b*x*dt) - (y*dt) - (z*x*dt)
                              znew = z + (-c*z*dt) + (x*y*dt)
                              (defaults: dt = .02, a = 5, b = 15, c = 1)
                              (Lorenz3D is the Lorenz Attractor with the
                              addition of 3D perspective transformations
                              as specified by the IFS <E>ditor's
                              transformation option)
  Rossler3d                   Orbit is solution to differential equation:
                              dx/dt = -y -z
                              dy/dt = x + a*y
                              dz/dt = b + x*z - c*z
                              Solution via first order Taylor series:
                              xnew = x - y*dt -   z*dt
                              ynew = y + x*dt + a*y*dt
                              znew = z + b*dt + x*z*dt - c*z*dt
                              Default params are dt=.04, a=.2, b=.2, c=5.7
  Henon                       Orbit generated by:
                              xnew =  1 + y - a*x*x
                              ynew =  b*x
                              The default parameters are a=1.4 and b=.3.
  Pickover                    Orbit generated by:
                              xnew = sin(a*y) - z*cos(b*x)
                              ynew = z*sin(c*x) - cos(d*y)
                              znew = sin(x)
                              Defaults: a=2.24, b=.43, c=-.65, d=-2.43
  Gingerbreadman              Orbit generated by:
                              xnew = 1 - y + |x|
                              ynew = x
  Diffusion                   See diffusion type description
  Julibrot                    See Julibrot type description


  fn(z*z)                     z(0)=pixel; z(n+1) = fn(z(n)*z(n))
  fn*fn                       z(0)=pixel; z(n+1) = fn(n)*fn(n)
  fn*z+z                      z(0)=pixel; z(n+1) = p1*fn(z(n))+p2*z(n)
  fn+fn                       z(0)=pixel; z(n+1)=p1*fn1(z(n))+p2*fn2(z(n))
  sqr(1/fn)                   z(0)=pixel; z(n+1) = (1/fn(z(n))*(1/fn(z(n))
  sqr(fn)                     z(0)=pixel; z(n+1) = fn(z(n))*fn(z(n))
  spider                      c(0)=z(0)=pixel; z(n+1) = z(n)*z(n) + c(n);
                              c(n+1) = c(n)/2 + z(n+1)
  manowar                     c = z1(0) = z(0) = Xcoord + i*Ycoord;
                              z(n+1) = z(n)^2 + z1(n) + c;
                              z1(n+1) = z(n);
  tetrate                     z(0) = c = pixel; z(n+1) = c^z(n)
  kamtorus, kamtorus3d        (See kamtorus type description for details)

  magnetj1,j2,m1,m2           (See type descriptions for details)

                     Fractint Version 15.0                     Page 89


  INSIDE=bof60|bof61

  Here is an *ATTEMPTED* explanation of what the inside=bof60 and
  inside=bof61 options do. This explanation is hereby dedicated to Adrian
  Mariano, who badgered it out of us! For the *REAL* explanation, see
  "Beauty of Fractals", page 62.

  Let p(z) be the function that is repeatedly iterated to generate a
  fractal using the escape-time algorithm.  For example, p(z) = z^2+c in
  the case of a Julia set. Then let pk(z) be the result of iterating the
  function p for k iterations. (The "k" should be shown as a superscript.)
  We could also use the notation pkc(z) when the function p has a
  parameter c, as it does in our example.  Now hold your breath and get
  your thinking cap on. Define a(c) = inf{|pck(0)|:k=1,2,3,...}. In
  English - a(c) is the greatest lower bound of the images of zero of as
  many iterations as you like. Put another way, a(c) is the closest to the
  origin any point in the orbit starting with 0 gets. Then the index (c)
  is the value of k (the iteration) when that closest point was achieved.
  Since there may be more than one, index(c) is the least such. Got it?
  Good, because the "Beauty of Fractals" explanation of this, is, ahhhh,
  *TERSE* ! Now for the punch line. Inside=bof60 colors the lake
  alternating shades according to the level sets of a(c).  Each band
  represents solid areas of the fractal where the closest value of the
  orbit to the origin is the same.  Inside=bof61 show domains where
  index(c) is constant.  That is, areas where the iteration when the orbit
  swooped closest to the origin has the same value. Well, folks, that's
  the best we can do! Improved explanations will be accepted for the next
  edition!


  FINITE ATTRACTORS (inside=attractor)

  Many of Fractint's fractals involve the iteration of functions of
  complex numbers until some "bailout" value is exceeded, then coloring
  the associated pixel according to the number of iterations performed.
  This process identifies which values tend to infinity when iterated, and
  gives us a rough measure of how "quickly" they get there.

  In dynamical terms, we say that "Infinity is an Attractor", as many
  initial values get "attracted" to it when iterated.  The set of all
  points that are attracted to infinity is termed The Basin of Attraction
  of Infinity.  The coloring algorithm used divides this Basin of
  Attraction into many distinct sets, each a single band of one color,
  representing all the points that are "attracted" to Infinity at the same
  "rate".  These sets (bands of color) are termed "Level Sets" - all
  points in such a set are at the same "Level" away from the attractor, in
  terms of numbers of iterations required to exceed the bailout value.

  Thus, Fractint produces colored images of the Level Sets of the Basin of
  Attraction of Infinity, for all fractals that iterate functions of
  Complex numbers, at least.  Now we have a sound mathematical definition
  of what Fractint's "bailout" processing generates, and we have formally
  introduced the terms Attractor, Basin of Attraction, and Level Set, so
  you should have little trouble following the rest of this section!

                     Fractint Version 15.0                     Page 90


  For certain Julia-type fractals, Fractint can also display the Level
  Sets of Basins of Attraction of Finite Attractors.  This capability is a
  by-product of the implementation of the MAGNETic fractal types, which
  always have at least one Finite Attractor.

  Most Julia-types that have a "lake" (normally colored blue by default)
  have a Finite Attractor within this lake, and the lake turns out to be,
  quite appropriately, the Basin of Attraction of this Attractor.

  The "inside=attractor" option (command-line or <Y> options screen)
  instructs Fractint to seek out and identify a possible Finite Attractor
  and, if found, to display the Level Sets of its Basin of Attraction, in
  addition to those of the Basin of Attraction of Infinity.  In many cases
  this results in a "lake" with colored "waves" in it;  in other cases
  there may be little change in the lake's appearance.

  For a quick demonstration, select a fractal type of LAMBDA, with a
  parameter of 0.5 + 0.5i.  You will obtain an image with a large blue
  lake.  Now set "inside=attractors" with the "X" menu. The image will be
  re-drawn with a much more colorful lake.  A Finite Attractor lives in
  the center of one of the resulting "ripple" patterns in the lake - turn
  the <O>rbits display on to see where it is - the orbits of all initial
  points that are in the lake converge there.

  Fractint tests for the presence of a Finite Attractor by iterating a
  Critical Value of the fractal's function.  If the iteration doesn't bail
  out before exceeding twice the iteration limit, it is almost certain
  that we have a Finite Attractor - we assume that we have.

  Next we define a small circle around it and, after each iteration, as
  well as testing for the usual bailout value being exceeded, we test to
  see if we've hit the circle. If so, we bail out and color our pixels
  according to the number of iterations performed.  Result - a nicely
  colored-in lake that displays the Level Sets of the Basin of Attraction
  of the Finite Attractor.  Sometimes !

  First exception : This does not work for the lakes of Mandel-types.
  Every point in a Mandel-type is, in effect, a single point plucked from
  one of its related Julia-types.  A Mandel-type's lake has an infinite
  number of points, and thus an infinite number of related Julia-type
  sets, and consequently an infinite number of finite attractors too.  It
  *MAY* be possible to color in such a lake, by determining the attractor
  for EVERY pixel, but this would probably treble (at least) the number of
  iterations needed to draw the image.  Due to this overhead, Finite
  Attractor logic has not been implemented for Mandel-types.

  Secondly, certain Julia-types with lakes may not respond to this
  treatment, depending on the parameter value used.  E.g., the Lambda Set
  for 0.5 + 0.5i responds well; the Lambda Set for 0.0 + 1.0i does not -
  its lake stays blue.  Attractors that consist of single points, or a
  cycle of a finite number of points are ok.  Others are not.  If you're
  into fractal technospeke, the implemented approach fails if the Julia-
  type is a Parabolic case, or has Siegel Disks, or has Herman Rings.

                     Fractint Version 15.0                     Page 91

  However, all the difficult cases have one thing in common - they all
  have a parameter value that falls exactly on the edge of the related
  Mandel-type's lake.  You can avoid them by intelligent use of the
  Mandel-Julia Space-Bar toggle:  Pick a view of the related Mandel-type
  where the center of the screen is inside the lake, but not too close to
  its edge, then use the space-bar toggle.  You should obtain a usable
  Julia-type with a lake, if you follow this guideline.

  Thirdly, the initial implementation only works for Julia-types that use
  the "Standard" fractal engine in Fractint.  Fractals with their own
  special algorithms are not affected by Finite Attractor logic, as yet.

  Despite these restrictions, the Finite Attractor logic can produce
  interesting results.  Just bear in mind that it is principally a bonus
  off-shoot from the development of the MAGNETic fractal types, and is not
  specifically tuned for optimal performance for other Julia types.

  (Thanks to Kevin Allen for the above).


  The following trig identities are invaluable for coding fractals that
  use complex-valued transcendental functions.

     e^(x+iy) = (e^x)cos(y) + i(e^x)sin(y)
     sin(x+iy) = sin(x)cosh(y) + icos(x)sinh(y)
     cos(x+iy) = cos(x)cosh(y) - isin(x)sinh(y)
     sinh(x+iy) = sinh(x)cos(y) + icosh(x)sin(y)
     cosh(x+iy) = cosh(x)cos(y) + isinh(x)sin(y)
     ln(x+iy) = (1/2)ln(x*x + y*y) + i(arctan(y/x) + 2kPi)
                                      (k = 0, +-1, +-2, +-....)

                       sin(2x)               sinh(2y)
     tan(x+iy) = ------------------  + i------------------
                 cos(2x) + cosh(2y)     cos(2x) + cosh(2y)

                      sinh(2x)                sin(2y)
     tanh(x+iy) = ------------------ + i------------------
                  cosh(2x) + cos(2y)    cosh(2x) + cos(2y)

         z^z = e^(log(z)*z)
         log(x + iy) = 1/2(log(x*x + y*y) + i(arc_tan(y/x))
         e^(x + iy) = (cosh(x) + sinh(x)) * (cos(y) + isin(y))
                     = e^x * (cos(y) + isin(y))
                     = (e^x * cos(y)) + i(e^x * sin(y))

                     Fractint Version 15.0                     Page 92

 Appendix B  Stone Soup With Pixels: The Authors

  Once upon a time, somewhere in Eastern Europe, there was a great famine.
  People jealously hoarded whatever food they could find, hiding it even
  from their friends and neighbors. One day a peddler drove his wagon into
  a village, sold a few of his wares, and began asking questions as if he
  planned to stay for the night.

  [No!  No!  It was three Russian Soldiers! - Lee Crocker]
  [Wait!  I heard it was a Wandering Confessor! - Doug Quinn]
  [Well *my* kids have a book that uses Russian Soldiers! - Bert]
  [Look, who's writing this documentation, anyway? - Monte]
  [Ah, but who gets it *last* and gets to upload it? - Bert]

  "There's not a bite to eat in the whole province," he was told. "Better
  keep moving on."

  "Oh, I have everything I need," he said. "In fact, I was thinking of
  making some stone soup to share with all of you." He pulled an iron
  cauldron from his wagon, filled it with water, and built a fire under
  it. Then, with great ceremony, he drew an ordinary-looking stone from a
  velvet bag and dropped it into the water.

  By now, hearing the rumor of food, most of the villagers had come to the
  square or watched from their windows. As the peddler sniffed the "broth"
  and licked his lips in anticipation, hunger began to overcome their
  skepticism.

  "Ahh," the peddler said to himself rather loudly, "I do like a tasty
  stone soup. Of course, stone soup with CABBAGE -- that's hard to beat."

  Soon a villager approached hesitantly, holding a cabbage he'd retrieved
  from its hiding place, and added it to the pot. "Capital!" cried the
  peddler. "You know, I once had stone soup with cabbage and a bit of salt
  beef as well, and it was fit for a king."

  The village butcher managed to find some salt beef...and so it went,
  through potatoes, onions, carrots, mushrooms, and so on, until there was
  indeed a delicious meal for all. The villagers offered the peddler a
  great deal of money for the magic stone, but he refused to sell and
  traveled on the next day. And from that time on, long after the famine
  had ended, they reminisced about the finest soup they'd ever had.

                                  ***

  That's the way Fractint has grown, with quite a bit of magic, although
  without the element of deception. (You don't have to deceive programmers
  to make them think that hours of painstaking, often frustrating work is
  fun... they do it to themselves.)

  It wouldn't have happened, of course, without Benoit Mandelbrot and the
  explosion of interest in fractal graphics that has grown from his work
  at IBM. Or without the example of other Mandelplotters for the PC. Or
  without those wizards who first realized you could perform Mandelbrot
  calculations using integer math (it wasn't us - we just recognize good

                     Fractint Version 15.0                     Page 93

  algorithms when we steal--uhh--see them).  Or those graphics experts who
  hang around the Compuserve PICS forum and keep adding video modes to the
  program.  Or...


  A WORD ABOUT THE AUTHORS

  Fractint is the result of a synergy between the main authors, many
  contributors, and published sources.  All four of the main authors have
  had a hand in many aspects of the code.  However, each author has
  certain areas of greater contribution and creativity.  Since there is
  not room in the help screen for the contributions of the main authors,
  we list these here to facilitate those who would like to communicate
  with us on particular subjects.

  Bert Tyler is the original author.  He wrote the "blindingly fast" 386-
  specific 32 bit integer math code and the original video mode logic.
  More than any of the authors, he has personally touched and massaged the
  entire source. His forte is writing fast 80x86 assembler, his knowledge
  of a variety of video hardware, and his skill at hacking up the code we
  send him!

  Bert has a BA in mathematics from Cornell University.  He has been in
  programming since he got a job at the computer center in his sophomore
  year at college - in other words, he hasn't done an honest day's work in
  his life.  He has been known to pass himself off as a PC expert, a UNIX
  expert, a statistician, and even a financial modeling expert.  He is
  currently masquerading as an independent PC consultant, supporting the
  PC-to-Mainframe communications environment at NIH.  If you sent mail
  from the Internet to an NIH staffer on his 3+Mail system, it was
  probably Bert's code that mangled it during the Internet-to-3+Mail
  conversion.  He also claims to support the MS-Kermit environment at NIH.
  Fractint is Bert's first effort at building a graphics program.

  Tim Wegner contributed the original implementation of palette animation,
  and is responsible for most of the 3D mechanisms.  He provided the main
  outlines of the "StandardFractal" engine and data structures, and is
  accused by his cohorts of being "obsessed with options".  Tim is quite
  proud of having originally integrated the 256 color super VGA modes in
  Fractint, especially since he knows almost nothing about it!

  Tim has BA and MA degrees in mathematics from Carleton College and the
  University of California Berkeley.  He worked for 7 years overseas as a
  volunteer, doing things like working with Egyptian villagers building
  water systems. Since returning to the US in 1982, he has written shuttle
  navigation software, a software support environment prototype, and
  supported strategic information planning, all at NASA's Johnson Space
  Center.

  Mark Peterson invented the periodicity detection logic, several original
  fractal types, transcendental function libraries, alternate math
  implementations, the formula compiler, and the "Julibrot" intrinsic 3D
  fractals - in other words, most of the truly original ideas in Fractint!

                     Fractint Version 15.0                     Page 94

  Mark's knowledge of higher mathematics and programming was achieved
  almost entirely through self-study.  Currently he works as a real-time
  supervisor of the electrical transmission system for Connecticut and
  Massachusetts. When not hard at work on programming projects he relaxes
  with Karate and Judo.

  Pieter Branderhorst is a late-comer to the group who likes to distract
  the other authors with enhancements impacting at least 1/2 of the source
  files at once.  His contributions include super solid guessing, image
  rotation, resume, and fast disk caching.

  Pieter left high school to work with computers, back when huge machines
  had 64k of core.  He's been happily computing since, mostly programming
  and designing software from comms firmware to database and o/s, and
  anything between, and large scale online transaction processing
  applications.  He has worked as a free-lance computer consultant
  (whatever that means) since 1983.


  Accessing the Authors
  ======================================

  Communication between the authors for development of the next version of
  Fractint takes place in COMART (Computer Art) Section 15 (Fractals) of
  CompuServe (CIS).  Access to this area is open to any and all interested
  in computer generated fractals.  Stop on by if you have any questions or
  just want to take a peek at what's getting tossed into the soup!

  Also, you'll find many GIF image files generated by fellow Fractint fans
  and many fractal programs as well in that forum's data library 15.

  The following authors have agreed to the distribution of their
  addresses. Usenet/Internet/Bitnet/Whatevernet users can reach CIS users
  directly if they know the user ID (i.e., Bert Tyler can be reached as
  [e-mail]).

  Just remember that CIS charges by the minute, so it costs us a little
  bit to read a message -- don't kill us with kindness. And don't send all
  your mail to Bert -- spread it around a little!

  Main authors:

  Bert Tyler              [73477,433] on CIS
  Tyler Software          btyler on BIX
  124 Wooded Lane
  Villanova, PA 19085
  [phone]

  Timothy Wegner          [71320,675] on CIS
  4714 Rockwood           [e-mail] on Internet
  Houston, TX 77004       [e-mail] on Internet
  [phone]

                     Fractint Version 15.0                     Page 95

  Mark Peterson           [70441,3353] on CIS
  The Yankee Programmer
  405-C Queen St., Suite #181
  Southington, CT 06489
  [phone]

  Pieter Branderhorst     [72611,2257] on CIS
  Amthor Computer Consultants
  3915 Bedford Rd.
  Victoria, B.C., Canada V8N 4K6
  [phone]


  Contributing authors (list alphabetically);

  Joseph A Albrecht
  9250 Old Cedar Ave #215
  Bloomington, Mn 55425
  [phone]

  Kevin Allen
  PO Box 335
  Seven Hills
  NSW 2147
  Australia

  Rob Beyer               [71021,2074] on CIS
  23 Briarwood Lane
  Laguna Hills, CA, 92656
  [phone]
  (7-12pm PST & weekends)


  Michael D. Burkey       [e-mail] on Internet
  6600 Crossgate Rd.
  Knoxville, TN 37912

  Lee Daniel Crocker      [73407,2030] on CIS
  1380 Jewett Avenue      lcrocker on BIX
  Pittsburg, CA 94565     ames!pacbell!sactoh0!siva!lee on Usenet
  [phone]

  Monte Davis             [71450,3542] on CIS
  31 Washington St
  Brooklyn, NY 11201
  [phone]

  Richard Finegold        [76701,153] on CIS
  1414 179th Ave NE       [e-mail] on InterNET
  Bellevue, WA 98008      uw-beaver!blake!richg on UseNET
  [phone]

  David Guenther          [70531,3525] on CIS
  50 Rockview Drive
  Irvine, CA 92715

                     Fractint Version 15.0                     Page 96


  Michael L. Kaufman      [71610,431] on CIS
  2247 Ridge Ave, #2K     (also accessible via EXEC-PC bbs)
  Evanston, IL, 60201
  [phone]

  Adrian Mariano           [e-mail] on INTERNET
  2729 72nd AVE SE
  Mercer Island, WA 98040

  Joe McLain              [75066,1257] on CIS
  McLain Imaging
  2417 Venier
  Costa Mesa, CA 92627
  [phone]

  Bob Montgomery          [73357,3140] on CIS
  (Author of VPIC)
  132 Parsons Road
  Longwood, Fl  32779

  Ethan Nagel             [70022,2552] on CIS
  PO Box 7
  Yarnell, Arizona 85362
  [phone]


  Marc Reinig             [72410,77] on CIS
  3415 Merrill Rd.        [e-mail]!daver!cypress on Usenet
  Aptos, CA. 95003        abu on BIX
  [phone]

  Lee H. Skinner
  P.O. Box 14944
  Albuquerque, NM  87191

  Dean Souleles           [75115,1671] on CIS
  8840 Collett Ave.
  Sepulveda, CA  91343
  [phone]

  Scott Taylor                  [72401,410] on CIS
  1901 South County Road 23E    DGWM18A on Prodigy
  Berthoud, CO 80513
  [phone]

  Paul Varner             [73237,441] on CIS
  PO Box 930
  Shepherdstown, WV 25443
  [phone]

  Phil Wilson             [76247,3145] on CIS
  410 State St., #55
  Brooklyn, NY 11217
  [phone]

                     Fractint Version 15.0                     Page 97

 Appendix C  Revision History

  Features first appearing in:
  ===========================

  Version 14    8/90

  LAST MINUTE NEWS FLASH!
    Compuserve announces the GIF89a on August 1, 1990, and Fractint
    supports it on August 2! GIF files can now contain fractal
    information!  Fractint now saves its files in the new GIF89a format by
    default, and uses .GIF rather than .FRA as a default filetype.  Note
    that Fractint still *looks* for a .FRA file on file restores if it
    can't find a .GIF file, and can be coerced into using the old GIF87a
    format with the new 'gif87a=yes' command-line option.

  Pieter Branderhorst mounted a major campaign to get his name in lights:
  Mouse interface:  Diagonals, faster movement, improved feel. Mouse
    button assignments have changed - see the online help.
  Zoom box enhancements:  The zoom box can be rotated, stretched, skewed,
    and panned partially offscreen.  See "More Zoom Box Commands".
  FINALLY!! You asked for it and we (eventually, by talking Pieter into it
    [actually he grabbed it]) did it!  Images can be saved before
    completion, for a subsequent restore and continue.  See "Interrupting
    and Resuming" and "Batch Mode".
  Off-center symmetry:  Fractint now takes advantage of x or y axis
    symmetry anywhere on the screen to reduce drawing time.
  Panning:  If you move an image up, down, left, or right, and don't
    change anything else, only the new edges are calculated.
  Disk-video caching - it is now possible, reasonable even, to do most
    things with disk video, including solid guessing, 3d, and plasma.
  Logarithmic palette changed to use all colors.  It now matches regular
    palette except near the "lake".  "logmap=old" gets the old way.
  New "savetime=nnn" parameter to save checkpoints during long
    calculations.
  Calculation time is shown in <Tab> display.

  Kevin Allen, of Antipodean origin, did the following:
  Made Bifurcation/Verhulst into a generalized Fractal Engine (like
    StandardFractal, but for Bifurcation types), and implemented
    periodicity checking for Bifurcation types to speed them up.
  Added Integer version of Verhulst Bifurcation (lots faster now). Integer
    is the default.  The Floating-Point toggle works, too.
  Added NEW Fractal types BIFLAMBDA, BIF+SINPI, and BIF=SINPI. These are
    Bifurcation types that make use of the new Engine. Floating-
    point/Integer toggle is available for BIFLAMBDA. The SINPI types are
    Floating-Point only, at this time.
  Corrected the generation of the MandelLambda Set.  Sorry, but it's
    always been wrong (up to v 12, at least).  Ask Mandelbrot !
  Added NEW Fractal types MAGNET1M, MAGNET1J, MAGNET2M, MAGNET2J from "The
    Beauty of Fractals".  Floating-Point only, so far, but what do you
    expect with THESE formulae ?!
  Added new symmetry types XAXIS NOIMAG and XAXIS NOREAL, required by the
    new MAGNETic Fractal types.

                     Fractint Version 15.0                     Page 98

  Added Finite Attractor Bailout (FAB) logic to detect when iterations are
    approaching a known finite attractor. This is required by the new
    MAGNETic Fractal types.
  Added Finite Attractor Detection (FAD) logic which can be used by *SOME*
    Julia types prior to generating an image, to test for finite
    attractors, and find their values, for use by FAB logic. Can be used
    by the new MAGNETic Fractal Types, Lambda Sets, and some other Julia
    types too.

  Mike Burkey sent us new tweaked video modes:
    VGA     - 400x600x256   376x564x256   400x564x256
    ATI VGA - 832x612x256
  New HP Paintjet support from Chris Martin
  New "FUNCTION=" command to allow substition of different transcendental
    functions for variables in types (allows one type with four of these
    variables to represent 7*7*7*7 different types!
  ALL KINDS of new fractal types, some using "FUNCTION=": fn(z*z), fn*fn,
    fn*z+z, fn+fn, sqr(1/fn), sqr(fn), spider, tetrate, and Manowar. Most
    of these are generalizations of formula fractal types contributed by
    Scott Taylor and Lee Skinner.
  Distance Estimator logic can now be applied to many fractal types using
    distest= option. The types "demm" and "demj" have been replaced by
    "type=mandel distest=nnn" and "type=julia distest=nnn"
  Added extended memory support for diskvideo thanks to Paul Varner
  Added support for "center and magnification" format for corners.
  Color 0 is no longer generated except when specifically requested with
    inside= or outside=.
  Formula name is now included in <Tab> display and in <S>aved images.
  Bug fixes - formula type and diskvideo, batch file outside=-1 problem.
  Now you can produce your favorite fractal terrains in full color instead
    of boring old monochrome! Use the fullcolor option in 3d! Along with a
    few new 3D options.
  New "INITORBIT=" command to allow alternate Mandelbrot set orbit
    initialization.


  Version 13.0, 5/90

  F1 was made the help key.
    Use F1 for help
    Use F9 for EGA 320x200x16 video mode
    Use CF4 for EGA 640x200x16 mode (if anybody uses that mode)
  Super-Solid-guessing (three or more passes) from Pieter Branderhorst
    (replaces the old solid-guessing mode)
  Boundary Tracing option from David Guenther ("fractint passes=btm", or
    use the new 'x' options screen)
  "outside=nnn" option sets all points not "inside" the fractal to color
    "nnn" (and generates a two-color image).
  'x' option from the main menu brings up a full-screen menu of many
    popular options and toggle switches
  "Speed Key" feature for fractal type selection (either use the cursor
    keys for point-and-shoot, or just start typing the name of your
    favorite fractal type)
  "Attractor" fractals (Henon, Rossler, Pickover, Gingerbread)
  Diffusion fractal type by Adrian Mariano

                     Fractint Version 15.0                     Page 99

  "type=formula" formulas from Scott Taylor and Lee H. Skinner.
  "sound=" options for attractor fractals.  Sound=x  plays speaker tones
    according to the 'x' attractor value  Sound=y  plays speaker tones
    according to the 'y' attractor value.  Sound=z  plays speaker tones
    according to the 'z' attractor value  (These options are best invoked
    with the floating-point algorithm flag set.)
  "hertz=" option for adjusting the "sound=x/y/z" output.
  Printer support for color printers (printer=color) from Kurt Sowa
  Trident 4000 and Oak Technologies SuperVGA support from John Bridges
  Improved 8514/A support (the zoom-box keeps up with the cursor keys
    now!)
  Tandy 1000 640x200x16 mode from Brian Corbino (which does not, as yet,
    work with the F1(help) and TAB functions)
  The Julibrot fractal type and the Starmap option now automatically
    verify that they have been selected with a 256-color palette, and
    search for, and use, the appropriate GLASSESn.MAP or ALTERN.MAP
    palette map when invoked.  *You* were supposed to be doing that
    manually all along, but *you* probably never read the docs, huh?

  Bug Fixes:
    TAB key now works after R(estore) commands
    PS/2 Model 30 (MCGA) adapters should be able to select 320x200x256
    mode again (we think)
    Everex video adapters should work with the Autodetect modes again (we
    think)


  Version 12.0, 3/90

  New SuperVGA Autodetecting and VESA Video modes (you tell us the
    resolution you want, and we'll figure out how to do it)
  New Full-Screen Entry for most prompting
  New Fractal formula interpreter ('type=formula') - roll your own
    fractals without using a "C" compiler!
  New 'Julibrot' fractal type
  Added floating point option to all remaining fractal types.
  Real (funny glasses) 3D - Now with "real-time" lorenz3D!!
  Non-Destructive <TAB> - Check out what your fractal parameters are
    without stopping the generation of a fractal image
  New Cross-Hair mode for changing individual palette colors (VGA only)
  Zooming beyond the limits of Integer algorithms (with automatic
    switchover to a floating-point algorithm when you zoom in "too far")
  New 'inside=bof60', 'inside=bof61' ("Beauty of Fractals, Page nn")
    options
  New starmap ('a' - for astrology? astronomy?) transformation option
  Restrictions on the options available when using Expanded Memory
    "Disk/RAM" video mode have been removed
  And a lot of other nice little clean-up features that we've already
    forgotten that we've added...
  Added capability to create 3D projection images (just barely) for people
    with 2 or 4 color video boards.

                     Fractint Version 15.0                    Page 100

  Version 11.0, 1/90

  More fractal types
    mandelsinh/lambdasinh        mandelcosh/lambdacosh
    mansinzsqrd/julsinzsqrd      mansinexp/julsinexp
    manzzprw/julzzpwr            manzpower/julzpower
    lorenz (from Rob Beyer)      lorenz3d
    complexnewton                complexbasin
    popcorn

  Most fractal types given an integer and a floating point algorithm.
    "Float=yes" option now determines whether integer or floating-point
    algorithms are used for most fractal types.  "F" command toggles the
    use of floating-point algorithms, flagged in the <Tab> status display
  8/16/32/../256-Way decomposition option (from Richard Finegold)
  "Biomorph=", "bailout=", "symmetry="  and "askvideo=" options
  "T(ransform)" option in the IFS editor lets you select 3D options (used
    with the Lorenz3D fractal type)
  The "T(ype)" command uses a new "Point-and-Shoot" method of selecting
    fractal types rather than prompting you for a type name
  Bug fixes to continuous-potential algorithm on integer fractals, GIF
    encoder, and IFS editor


  Version 10.0, 11/89

  Barnsley IFS type (Rob Beyer)
  Barnsley IFS3D type
  MandelSine/Cos/Exp type
  MandelLambda/MarksLambda/Unity type
  BarnsleyM1/J1/M2/J2/M3/J3 type
  Mandel4/Julia4 type
  Sierpinski gasket type
  Demm/Demj and bifurcation types (Phil Wilson), "test" is "mandel" again
  <I>nversion command for most fractal types
  <Q>uaternary decomposition toggle and "DECOMP=" argument
  <E>ditor for Barnsley IFS parameters
  Command-line options for 3D parameters
  Spherical 3D calculations 5x faster
  3D now clips properly to screen edges and works at extreme perspective
  "RSEED=" argument for reproducible plasma clouds
  Faster plasma clouds (by 40% on a 386)
  Sensitivity to "continuous potential" algorithm for all types except
    plasma and IFS
  Palette-map <S>ave and Restore (<M>) commands
  <L>ogarithmic and <N>ormal palette-mapping commands and arguments
  Maxiter increased to 32,000 to support log palette maps
   .MAP and .IFS files can now reside anywhere along the DOS path
  Direct-video support for Hercules adapters (Dean Souleles)
  Tandy 1000 160x200x16 mode (Tom Price)
  320x400x256 register-compatible-VGA "tweaked" mode
  ATI VGA Wonder 1024x768x16 direct-video mode (Mark Peterson)
  1024x768x16 direct-video mode for all supported chipsets
  Tseng 640x400x256 mode
  "Roll-your-own" video mode 19

                     Fractint Version 15.0                    Page 101

  New video-table "hot-keys" eliminate need for enhanced keyboard to
    access later entries


  Version 9.3, 8/89

  <P>rint command and "PRINTER=" argument (Matt Saucier)
  8514/A video modes (Kyle Powell)
  SSTOOLS.INI sensitivity and '@THISFILE' argument
  Continuous-potential algorithm for Mandelbrot/Julia sets
  Light source 3D option for all fractal types
  "Distance estimator" M/J method (Phil Wilson) implemented as "test" type
  LambdaCosine and LambdaExponent types
  Color cycling mode for 640x350x16 EGA adapters
  Plasma clouds for 16-color and 4-color video modes
  Improved TARGA support (Joe McLain)
  CGA modes now use direct-video read/writes
  Tandy 1000 320x200x16 and 640x200x4 modes (Tom Price)
  TRIDENT chip-set super-VGA video modes (Lew Ramsey)
  Direct-access video modes for TRIDENT, Chips & Technologies, and ATI VGA
    WONDER adapters (John Bridges). and, unlike version 9.1, they WORK in
    version 9.3!)
  "zoom-out" (<Ctrl><Enter>) command
  <D>os command for shelling out
  2/4/16-color Disk/RAM video mode capability and 2-color video modes
    supporting full-page printer graphics
  "INSIDE=-1" option (treated dynamically as "INSIDE=maxiter")
  Improved <H>elp and sound routines (even a "SOUND=off" argument)
  Turbo-C and TASM compatibility (really!  Would we lie to you?)


  Version 8.1, 6/89

  <3>D restore-from-disk and 3D <O>verlay commands, "3D=" argument
  Fast Newton algorithm including inversion option (Lee Crocker)
  16-bit Mandelbrot/Julia logic for 386-class speed with non-386 PCs on
    "large" images (Mark Peterson)
  Restore now loads .GIF files (as plasma clouds)
  TARGA video modes and color-map file options (Joe McLain)
  30 new color-cycling palette options (<Shft><F1> to <Alt><F10>)
  "Disk-video, RAM-video, EMS-video" modes
  Lambda sets now use integer math (with 80386 speedups)
  "WARN=yes" argument to prevent over-writing old .GIF files


  Version 7.0, 4/89

  Restore from disk (from prior save-to-disk using v. 7.0 or later)
  New types: Newton, Lambda, Mandelfp, Juliafp, Plasma, Lambdasine
  Many new color-cycling options (for VGA adapters only)
  New periodicity logic (Mark Peterson)
  Initial displays recognize (and use) symmetry
  Solid-guessing option (now the default)
  Context-sensitive <H>elp
  Customizable video mode configuration file (FRACTINT.CFG)

                     Fractint Version 15.0                    Page 102

  "Batch mode" option
  Improved super-VGA support (with direct video read/writes)
  Non-standard 360 x 480 x 256 color mode on a STANDARD IBM VGA!


  Version 6.0, 2/89

  32-bit integer math emulated for non-386 processors; FRACT386 renamed
    FRACTINT
  More video modes


  Version 5.1, 1/89

  Save to disk
  New! Improved! (and Incompatible!) optional arguments format
  "Correct" initial image aspect ratio
  More video modes


  Version 4.0, 12/88

  Mouse support (Mike Kaufman)
  Dynamic iteration limits
  Color cycling
  Dual-pass mode
  More video modes, including "tweaked" modes for IBM VGA and register-
    compatible adapters


  Version 3.1, 11/88

  Julia sets


  Version 2.1, 10/23/88 (the "debut" on CIS)

  Video table
  CPU type detector


  Version 2.0, 10/10/88

  Zoom and pan


  Version 1.0, 9/88

  The original, blindingly fast, 386-specific 32-bit integer algorithm

                     Fractint Version 15.0                    Page 103

 Appendix D  Bibliography

  BARNSLEY, Michael: "Fractals Everywhere", Academic Press, 1988.

  DEWDNEY, A. K., "Computer Recreations" columns in "Scientific American"
     -- 8/85, 7/87, 11/87, 12/88, 7/89.

  FEDER, Jens: "Fractals", Plenum, 1988.
     Quite technical, with good coverage of applications in fluid
     percolation, game theory, and other areas.

  GLEICK, James: "Chaos: Making a New Science", Viking Press, 1987.
     The best non-technical account of the revolution in our understanding
     of dynamical systems and its connections with fractal geometry.

  MANDELBROT, Benoit: "The Fractal Geometry of Nature", W. H. Freeman &
     Co., 1982.
     An even more revised and expanded version of the 1977 work. A rich
     and sometimes confusing stew of formal and informal mathematics, the
     prehistory of fractal geometry, and everything else. Best taken in
     small doses.

  MANDELBROT, Benoit: "Fractals: Form, Chance, and Dimension", W. H.
     Freeman & Co., 1977
     A much revised translation of "Les objets fractals: forme, hasard, et
     dimension," Flammarion, 1975.

  PEITGEN, Heinz-Otto & RICHTER, Peter: "The Beauty of Fractals,"
     Springer-Verlag, 1986.
     THE coffee-table book of fractal images, knowledgeable on computer
     graphics as well as the mathematics they portray.

  PEITGEN, Heinz-Otto & SAUPE, Ditmar: "The Science of Fractal Images,"
     Springer-Verlag, 1988.
     A fantastic work, with a few nice pictures, but mostly filled with
     *equations*!!!

                     Fractint Version 15.0                    Page 104

 Appendix E  Other Programs


  WINFRACT. Bert Tyler has ported Fractint to run under Windows 3!  The
  same underlying code is used, with a Windows user interface.  Winfract
  has almost all the functionality of Fractint - the biggest difference is
  the absence of a zillion weird video modes.  Fractint for DOS will
  continue to be the definitive version.  Winfract is available from
  CompuServe in COMART Lib 15, as WINFRA.ZIP (executable) and WINSRC.ZIP
  (source).

  PICLAB, by Lee Crocker - a freeware image manipulation utility available
  from Compuserve in PICS Lib 14, as PICLAB.EXE.  PICLAB can do very
  sophisticated resizing and color manipulation of GIF and TGA files.  It
  can be used to reduce 24 bit TGA files generated with the Fractint
  "lightname" option to GIF files.


  FDESIGN, by Doug Nelson (CIS ID 70431,3374) - a freeware IFS fractal
  generator available from Compuserve in COMART Lib 15, and probably on
  your local BBS.  This program requires a VGA adapter and a Microsoft-
  compatible mouse, and a floating point coprocessor is highly
  recommended.  It generates IFS fractals in a *much* more intuitive
  fashion than Fractint.  It can also (beginning with version 3.0) save
  its IFS formulas in Fractint-style .IFS files.

                     Fractint Version 15.0                    Page 105

 Appendix F  Version13 to Version 14 Type Mapping


  A number of types in version 13 and earlier have been generalized in
  version 14. We have added a "backward compatibility" hook that
  (hopefully) automatically translates these to the new form when the old
  files are read. Files may be converted via:

     FRACTINT OLDFILE.FRA SAVENAME=NEWFILE.GIF BATCH=YES

  In a few cases the biomorph flag was incorrectly set in older files.  In
  that case, add "biomorph=no" to the command line.

  This procedure can also be used to convert any *.fra file to the new
  GIF89a spec, which now allows storage of fractal information.


  TYPES CHANGED FROM VERSION 13 -


  V13 NAME                V14 NAME + PARAMETERS
  --------                --------------------------------------

  LOGMAP=YES              LOGMAP=OLD   for identical Logmap type

  DEMJ                    JULIA DISTEST=nnn

  DEMM                    MANDEL DISTEST=nnn

                          Note: DISTEST also available on many other
  fractals

  MANSINEXP               MANFN+EXP FUNCTION=SIN

                          Note: New functions for this type are
                                cos sinh cosh exp log sqr

  JULSINEXP               JULFN+EXP FUNCTION=SIN

                          Note: New functions for this type are
                                cos sinh cosh exp log sqr

  MANSINZSQRD             MANFN+ZSQRD FUNCTION=SQR/SIN

                          Note: New functions for this type are
                                cos sinh cosh exp log sqr

  JULSINZSQRD             JULFN+ZSQRD FUNCTION=SQR/SIN

                          Note: New functions for this type are
                                cos sinh cosh exp log sqr

  LAMBDACOS               LAMBDAFN FUNCTION=COS

  LAMBDACOSH              LAMBDAFN FUNCTION=COSH

                     Fractint Version 15.0                    Page 106


  LAMBDAEXP               LAMBDAFN FUNCTION=EXP

  LAMBDASINE              LAMBDAFN FUNCTION=SIN

  LAMBDASINH              LAMBDAFN FUNCTION=SINH

                          Note: New functions for this type are
                                log sqr

  MANDELCOS               MANDELFN FUNCTION=COS

  MANDELCOSH              MANDELFN FUNCTION=COSH

  MANDELEXP               MANDELFN FUNCTION=EXP

  MANDELSINE              MANDELFN FUNCTION=SIN

  MANDELSINH              MANDELFN FUNCTION=SINH

                          Note: New functions for this type are
                                log sqr

  MANDELLAMBDA            MANDELLAMBDA INITORBIT=PIXEL

  POPCORN SYMMETRY=NONE   POPCORNJUL

  -------------------------------------------------------------

  Formulas from FRACTINT.FRM in version 13

  MANDELGLASS             MANDELLAMBDA INITORBIT=.5/0

  INVMANDEL               V13 divide bug may cause some image differences.

  NEWTON4                 V13 divide bug may cause some image differences.

  SPIDER                  V13 divide bug may cause some image differences.

  MANDELSINE              MANDELFN FUNCTION=SIN BAILOUT=50

  MANDELCOSINE            MANDELFN FUNCTION=COS BAILOUT=50

  MANDELHYPSINE           MANDELFN FUNCTION=SINH BAILOUT=50

  MANDELHYPCOSINE         MANDELFN FUNCTION=COSH BAILOUT=50

  SCOTTSIN PARAMS=nnn     FN+FN FUNCTION=SIN/SQR BAILOUT=nnn+3

  SCOTTSINH PARAMS=nnn    FN+FN FUNCTION=SINH/SQR BAILOUT=nnn+3

  SCOTTCOS PARAMS=nnn     FN+FN FUNCTION=COS/SQR BAILOUT=nnn+3

  SCOTTCOSH PARAMS=nnn    FN+FN FUNCTION=COSH/SQR BAILOUT=nnn+3

                     Fractint Version 15.0                    Page 107

  SCOTTLPC PARAMS=nnn     FN+FN FUNCTION=LOG/COS BAILOUT=nnn+3

  SCOTTLPS PARAMS=nnn     FN+FN FUNCTION=LOG/SIN BAILOUT=nnn+3

                          Note: New functions for this type are
                          sin/sin sin/cos sin/sinh sin/cosh sin/exp
                          cos/cos cos/sinh cos/cosh cos/exp
                          sinh/sinh sinh/cosh sinh/exp sinh/log
                          cosh/cosh cosh/exp cosh/log
                          exp/exp exp/log exp/sqr log/log log/sqr sqr/sqr

  SCOTTSZSA PARAMS=nnn    FN(Z*Z) FUNCTION=SIN BAILOUT=nnn+3

  SCOTTCZSA PARAMS=nnn    FN(Z*Z) FUNCTION=COS BAILOUT=nnn+3

                          Note: New functions for this type are
                          sinh cosh exp log sqr

  SCOTTZSZZ PARAMS=nnn    FN*Z+Z FUNCTION=SIN BAILOUT=nnn+3

  SCOTTZCZZ PARAMS=nnn    FN*Z+Z FUNCTION=COS BAILOUT=nnn+3

                          Note: New functions for this type are
                          sinh cosh exp log sqr

  SCOTTSZSB PARAMS=nnn    FN*FN FUNCTION=SIN/SIN BAILOUT=nnn+3

  SCOTTCZSB PARAMS=nnn    FN*FN FUNCTION=COS/COS BAILOUT=nnn+3

  SCOTTLTS PARAMS=nnn     FN*FN FUNCTION=LOG/SIN BAILOUT=nnn+3

  SCOTTLTC PARAMS=nnn     FN*FN FUNCTION=LOG/COS BAILOUT=nnn+3

                          Note: New functions for this type are
                          sin/cos sin/sinh sin/cosh sin/exp sin/sqr
                          cos/sinh cos/cosh cos/exp cos/sqr
                          sinh/sinh sinh/cosh sinh/exp sinh/log sinh/sqr
                          cosh/cosh cosh/exp cosh/log cosh/sqr
                          exp/exp exp/log exp/sqr log/log log/sqr sqr/sqr

  SCOTTSIC PARAMS=nnn     SQR(1/FN) FUNCTION=COS BAILOUT=nnn+3

  SCOTTSIS PARAMS=nnn     SQR(1/FN) FUNCTION=SIN BAILOUT=nnn+3

  TETRATE PARAMS=nnn      TETRATE BAILOUT=nnn+3

                          Note: New function type sqr(1/fn) with
                                sin cos sinh cosh exp log sqr

                          Note: New function type sqr(fn) with
                                sin cos sinh cosh exp log sqr