OS/2 Shareware BBS: Graphics/Graphics.zip/fractz.zip/READ.ME

Text File | 1994-01-19 | 16KB | 280 lines

                                   FRACTZ


 I. Introduction

 FRACTZ is a fractal drawing program for the OS/2 Presentation Manager.  It is
 the result of a project I undertook solely for the purpose of learning how to
 program for OS/2.  There are PM programming details within FRACTZ that had me
 stumped for weeks on end.  The answers are out there, but finding them can be
 difficult and time consuming.  It is for this reason that I decided to donate
 it to the public, lock-stock-and-barrel, in the hopes of smoothing the bumps
 for anyone thinking of taking the same venture.  I also hope that some are
 inspired by the beauty in fractals.  They are an amazing area where science
 meets art.


 II.  Legal

 The executable file, the C source code, and the assorted ancillary files are
 free, but I retain the ownership and copyright.  The program is designed to
 run on any machine running OS/2 2.0 or higher, but it carries no guarantee of
 any kind.


 III.  The Beginning

 I am a fan of OS/2 and I am a programmer, but I'm not professionally into PM
 programming.  It was something I wanted to learn, so about a year ago I
 purchased both the IBM and Borland OS/2 compilers.  I also needed a project
 to start up my learning ramp.  I've always admired the beauty of fractals and
 have been long time fan of FRACTINT.  For those that don't know, FRACTINT is
 a free DOS fractal drawing program that has been worked on by numerous
 people.  Collectively they are known as the Stone Soup Group.  The name
 springs from an interesting parable, which I'll leave up to you to find and
 read.  There are now versions of FRACTINT for Windows and even OS/2.

 Another reason for choosing a fractal program was that I already had some DOS
 C code that I had started on some years ago, but had given up as being too
 much work.  You will probably see some remnants of this program in FRACTZ,
 like in the identifier "int".  Lastly, and most importantly from a technical
 point, I owned and had almost memorized the Waite book "Fractal Creations" by
 Tim Wegner and Mark Peterson.  These are two Stone Soup Group members and it
 is the definitive book for doing fractals on a PC.  A second edition of this
 book is now out.  I haven't seen it, but I understand it is much improved,
 although I don't see how.  Lastly, I would like to mention Bert Tyler.  He is
 the guy that shook the bushes that started the stampede.  Some of his
 personal suggestions are incorporated into FRACTZ.

 The Stone Soup Group hangs out on Compuserve in the GRAPHDEV forum, and I
 have gone to them on more than several occasions for technical details.  They
 are always willing to help.  One thing I need to mention is that the ASCII
 text color maps that are in the FRACTZ package came from FRACTINT.  I am
 including them with the permission of the Stone Soup Group.  That is
 something I couldn't do if FRACTZ wasn't free.


 IV.  The PM program and Some Caveats

 As I wrote this program, I did not envision it going anywhere.  It was
 strictly a learning effort on my part.  For that reason, it may not work
 properly on your machine.  I use a 486/33DX which has a Tseng ET4000 running
 at 800X600 resolution with 256 colors.  The .EXE file has in-line FPU code
 and I don't know what it will do on a machine without an FPU.  I wouldn't
 attempt this without an FPU anyway.  A similar statement holds about using
 it with a different numbers of colors or resolution.  It should work, but I
 just don't know.  I didn't write it to run on different machines and have
 never seen it attempted.

 Unfortunately, the fractal calculations are incredibly slow.  This is
 something which I attribute to a number of reasons.  The first is that I used
 type "complex" to ease the coding burden.  (FRACTINT, on the other hand,
 makes use of type long int.)  Type "complex" is one of the reasons it is a
 C++ program, although it is not OOP.  I looked at some compiled code and was
 horrified, but that is another subject.  Secondly, to reach a color depth of
 255, you may need to iterate up to 256 times at each pixel.  Thus, it may be
 necessary to evaluate a complex expression some 800X600X256 times in the
 worst case.  Take that number and multiply by the horrendous machine code and
 you will understand the problem.

 One nice thing about OS/2 of course, is that you can just move the fractal
 window out of the way and go on about other things.  However, I need to bring
 up a word of caution here.  If you change the aspect ratio of the window, the
 fractal will tear.  I know it is possible to bit-blast from one sized
 rectangle to another, but in this case, you will actually change the equation
 of the fractal while it is in the process of being computed.  That's why it's
 a no-no.  There may be a way of doing this without tearing the fractal, but I
 think it would involve calculating out-of-window points and I don't think
 that would be a good idea.


 V. Technical

 I can only give a sampling on fractals, as you really need a book.  All of
 the fractals in FRACTZ are what is known as "escape-time" fractals with one
 or two also possessing "finite-attracters".  One of the most famous is the
 Mandelbrot.  It's entire description is contained in this one "simple"
 equation:

     z = z*z + c

 This is an iterative equation with both z and c being complex numbers of the
 form (x+iy), i.e.  they correspond to points on the screen (or window) of
 your CRT.  The point, c, is the independent variable which comes from
 scanning horizontally in x then vertically in y. The first z point, z0, is
 taken to be the origin, or (0,0).  Thus, given a c (a particular pixel), one
 simply computes z1, z2, z3....  until one of two things happen.  1) You
 escape outside a circle of radius = 2 (hence the "escape-time" name) or 2)
 you never escape and are cut-off by some other criteria for maximum number of
 iterations.  This is called MAXITER and it is usually taken as some number
 say of at least 100.  The default in FRACTZ is the color depth, 255.  Thus,
 the color of a pixel (or more accurately the index into the RGB color table)
 is simply the number of iterations it takes to escape.  If it hits MAXITER
 without escaping, it is a color of your choosing.

 The Mandelbrot equation never converges, but some escape-time equations do.
 Such equations actually have a finite number of roots that will be found with
 the above iteration scheme.  These are the finite-attracters, and there are
 a few of these in FRACTZ.  This fractal type simply adds one more cutoff
 criterion of "have I converged on a root?".

 I'm sure one can see from the above expression why I chose type complex, but
 the simplicity totally belies what's hidden within.  Clearly, it is also easy
 to add additional fractal formulas, being largely a matter of adding a
 one-line case to a switch statement.


 VI.  Operation

 I don't have an installation procedure.  I would recommend installing FRACTZ
 in its own directory and using a program template to create a desktop object.
 FRACTZ will look for the color maps (*.MAP files) in its own directory.  Not
 finding any will cause it to generate a random map, and that map is not very
 pretty.  Also, remember you will be unzipping .C, .RC, etc.  so there are a
 good number of files.  There are even some bitmap files I created with
 FRACTZ.  I use one for my shutdown screen.  The program comes up running.
 In fact, you can't stop it.  The (background) fractal engine thread runs
 full-speed all the time and is drawing to a memory PS.  There is another
 small thread that wakes up from a DosSleep every few seconds and blasts the
 bits from a memory PS to the VDT.  Hence it appears to jump every time this
 thread wakes up.

 There is no real help once you are up and running.  I only hope the menus and
 dialogs are obvious enough.  Having previous experience with FRACTINT would
 be a big help here.

 First, the mouse operations:

    1. LMB (left mouse button) diagonal drag creates a "zoom box".  This will
    be the new window when you release the button.  A tiny box will act as a
    cancel.

    2. LMB double-click clears the window to black and restarts the
    calculation.

    3. RMB click will start a Julia fractal with initial conditions based on
    the (x,y) location of the mouse pointer.  Again, pick an interesting (e.g.
    ragged) area to click.

 There are not very many fractal types to choose from in the menu, but I think
 you will be surprised at how much you can do with these.  Notice that you can
 save-to/restore-from a BMP (bitmap file) at any time.  Look at some of the
 ones that I supplied.  This will not destroy any preceding calculations as
 they are being written to a memory PS.  These bitmaps are the 2.x variety and
 you can look at any 2.x bitmap.  I did not bother supporting 1.x bitmap,
 although it shouldn't be hard to add.  Note that you cannot restart a
 calculation from a BMP file, although it is something I have considered
 adding.  For now, you can only "un-view" it to get back to where you were.

 The next menu item is the display option.  By all means check out the
 "orbits" option, but turn out the lights first.  I was really surprised by
 how well this turned out.  Books rarely mention this feature because the
 "neatness" is all in the dynamics.  Also, it is hard to do without multiple
 presentation spaces, so thanks IBM.  Take a look before you zoom in or you
 may not see much.  That is not because the "fractoids" aren't there, but
 probably because they are orbiting over your neighbor's house or even over
 another city.  These orbits come straight from the fractal engine and this
 option will slow it down a lot, but it's worth it.

 The "change colors" option comes from my somewhat feeble attempt to imitate
 FRACTINT's color cycling option.  FRACTINT grabs the hardware video registers
 to create a dazzling color show.  That is something I couldn't do, but I left
 this option in anyway.  Basically, it runs small color wavelets up and down
 the RGB table to produce somewhat smooth and somewhat random time-color
 variations.

 The Settings option produces the only dialog box in FRACTZ.  This is a hard
 option to get across in a README, so I hope probing around will be more
 fruitful than what I can say here.  The Box Coordinates define the scale of
 the fractal and are XL, XR, YB, YT for x-left, x-right, y-bottom, y-top.
 Normally, you don't enter these.  They start at some default and change as
 you zoom in.

 The perturbations, called Real Pert.(dX) and Imag. Pert.(dY) in the
 dialog box, are a way of throwing a twist into the fractal calculations.
 Again, I would suggest the book (or the C source) to see what they really do.
 It is not necessary to mess with them except in the case of the Lambda
 fractal.  For that, start with some- thing close to what is in the "hint
 box".

 The "Maxiter" that is in the dialog box is the iteration cutoff and has
 already been discussed.  It defaults to the (my) color depth of 255.
 Changing it to something like 150 will speed things up, but reduce the number
 of colors.  The Bailout term is the radius of the bailout circle where
 calculations are stopped.  That is, the fractoid has "escaped" if abs(z) >
 bailout.  Please note - the FRACTINT authors (and the book) use "bailout" to
 mean the square of the radius so that they can avoid a square root operation.
 I.E.  FRACTINT tests if (x**2 + y**2 > bailout).  Thus you will see their
 value of bailout is 4 where I use 2.

 The dialog item "Inside" is what sets the RGB color if the iteration hits
 Maxiter before escaping.  The term "inside" comes from the lake-like feature
 in the center of the Mandelbrot fractal.  Any iteration that starts within
 the lake will not escape.  "Inside" means inside the lake and the default
 value is 1 which is blue.  However, if you switch to 3-D mode, I would
 suggest making the value 255.  This will switch the lake to a mountain
 plateau.

 There is a check box called "use potential".  I think this is a method based
 on some formula from potential theory, but whatever the case, the purpose is
 to smooth out a fractal image for making 3-D renderings.  The idea is that
 instead of using the count value when a fractoid escapes, you use the
 logarithm of the radius after it escapes.  Sorry, I never did get this to
 work properly.

 The next two regions of the dialog box are for doing spherical projections
 and 3-D surfaces.  You can also do 3-D spheres.  The purpose of the
 "covers-180" versus "covers-360" determines how much of the spherical fractal
 you want to see.  180 degrees will show all, but will show as a hemisphere if
 you also select 3-D.

 The box labeled "Ceiling Ht."  is what scales the height of the fractal in
 3-D.  FRACTZ uses color as the height, so some number larger than 255 is
 required in order to see the full picture.  I have used values greater than
 2,000 in order to "flatten" the mountains.

 Lastly come the rotation angles.  Alpha, beta, and phi are the rotation
 angles about x,y, and z using the right-hand rule (this z is perpendicular to
 the x-y plane.  It is not the complex z).  However, before doing the
 rotation, I flipped the fractal to view it edge on.  In other words, for
 rotation angles of (0,0,0), you would see the fractal with the x-axis
 horizontal and increasing to the right, the z-axis (color) would be vertical
 and increasing upward, and the y-axis would be normal to the screen and
 increasing in the direction you are viewing.  By doing this, I get best
 results by keeping all angles somewhat small, about (+/-) 15-20 degrees or
 so.  This is somehow more palatable to me than using rotation angles like 75
 degrees.

 If you switch into 3-D, you need to start with a completely clear, black
 window.  Double click the left mouse button to do this as it does not happen
 automatically.  It used to, but I shot myself in the foot too many times.
 The reason it needs black is that the 3-D option uses a ray tracing technique
 to not have background objects write over foreground objects.  When the
 program encounters a 3-D black pixel, it means "I haven't been here yet",
 which is something it needs to know in order to work properly.  By the way, I
 think the Julia fractals have the most interesting 3-D shapes.  I should also
 mention here that a phi-rotation is a rotation about the polar axis in
 spherical coordinates.

 The last menu item is choice of color map.  Unlike what FRACTINT does, I
 elected to hard code the file names right into the code.  Yes, I know, this
 is not a good programming practice, but it is particularly effective.
 These are small files, and because we all have a good diskcache, you get
 almost immediate response with one click.  These maps are a work of art in
 themselves and my hat is off to the Stone Soup Group again.  They can bring
 out surprising details you just can't see any other way.  Always try some of
 the color maps if you feel like you are getting bored.

 Well, enough has been said.  I hope it is understandable and that someone can
 make use of this.  If you have any questions, I will be glad to answer what I
 can.  I am usually around OS2DF1 on Compuserve.


 Tom Stokes

 1/19/94

 CIS id 73770,3577