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**********************************
*................................*
*. .*
*. .*
*. A Guide to Using .*
*. .*
*. FRACTINT .*
*. .*
*. PART II .*
*. .*
*. .*
*. (for Version 15.1) .*
*. .*
*. .*
*................................*
**********************************
A TOY FOR PEOPLE WHO THINK
(brought to you by the Ideal Studies BBS)
-------------------------------------------------------
NONLINEAR DYNAMICS, FRACTAL GEOMETRY, CELLULAR AUTOMATA
Worcester, MA (508) 757-1806 Sysop: Peter Longo
-------------------------------------------------------
(and by reed/write & Company)
February, 1991
Version 1.0
=======================
= =
= Table of Contents =
= =
=======================
ADAPTER=c|e|m 4
AMBIENT=nnn (0 - 100) 5
ASKVIDEO=y|n 7
BAILOUT=nnn 8
BATCH=y 10
BATCH=config 13
BIOMORPH=nnn 22
BRIGHT=nn/nn 24
CENTER-MAG=Xctr/Yctr/Mag 26
COMPORT=port/baud/options 27
CONVERGE=nn 28
CORNERS=xmin/xmax/ymin/ymax[/x3rd/y3rd] 29
CROP=nn/nn/nn/nn 33
CYCLELIMIT=nnn 34
DECOMP=2|4|8|16|32|64|128|256 35
DISTEST=nnn 37
EPSF=1|2|3 39
EXITMODE=nn 40
FILENAME=name 41
FILLTYPE=nn 43
FINATTRACT=y 44
FLOAT=y 46
FORMULAFILE=formulafilename 48
FULLCOLOR=y|1 62
FUNCTION=sin|cos|sinh|cosh|exp|log|sqr 63
GIF87a=y 66
HALFTONE=freq/angle/style 67
HAZE=nnn (0 - 100) 68
HERTZ=nnn 69
IFS=filename 70
IFSCODES=N/a/b/c/d/e/f/g/h 75
INITORBIT=nnn/nnn 76
INSIDE=0|-1|nnn|bof60|bof61 87
INTEROCULAR=nn 91
INVERT=radius/xcenter/ycenter 92
Table of Contents (Continued)
ITERINCR=nnn 94
LATITUDE=nn/nn 95
LFILE=lsystemfile 97
LNAME=lsystemname 97
LIGHTNAME=<filename> 105
LIGHTSOURCE=xx/yy/zz 107
LOGMAP=y|old|n 109
LONGITUDE=nn/nn 111
MAP=filename 112
MAXITER=nnn 115
OUTSIDE=nnn 116
OVERWRITE=n|y 117
PARAMS=n/n/n/n... 118
PASSES=1|2|g|b 121
PERIODICITY=no|show|nnn|-nnn 123
PERSPECTIVE=nn 124
POTENTIAL=maxcolor[/slope[/modulus[/16bit]]] 126
PREVIEW=y 129
PRINTER=type[/resolution[/port#]] 130
RADIUS=nn 135
RANDOMIZE=n 136
ROTATION=xrot[/yrot[/zrot]] 137
ROUGHNESS=nn 138
RSEED=nnnn 139
SAVENAME=name 140
SAVETIME=nnn 141
SCALEZYZ=nn/nn/nn 142
@SET 143
SHIFT=xshift/yshift 144
SMOOTHING=nn 145
SOUND=off|x|y|z 146
SPHERE=y 147
STEREO=n 148
SYMMETRY=xxx 149
TEXTCOLORS=aa/bb/cc/... 150
TEXTSAFE=y|n 153
3D=y 154
TITLE=y 157
TRANSLATE=y|-n|n 158
TRANSPARENT=min/max 159
TYPE=typename 160
VIDEO=xxx 161
WARN=y|n 162
WATERLINE=nn 163
XYADJUST=nn/nn 164
XYSHIFT=nn/nn 164
Preface
This is basically a draft of Part II of this Guide. It has NOT been
reviewed by the folks who are part of the Stone Soup Group on CompuServe,
mainly because none of them has the time to work on a project of this
size. However, Part II is more than 95% accurate and at any rate there
are no critical points where an error will cause you severe problems.
The point of Fractint is to have fun and the purpose of this manual is
to help you to do so by making all of the options understandable and
therefore available for your use.
Please, please get back to us with any suggested changes of any kind.
======================================================================
A Guide to Fractint: Part II
======================================================================
This volume of the Guide will cover all of Fractint's options. These
will be presented in order by the name which is used to set or select
the option in batch mode. Any options which have no corresponding
batch parameter will be inserted in alphabetic order with a comment
stating that there is no batch argument.
A batch argument is one which may be used on the DOS command line when
Fractint is executed. For example,
fractint map=chroma
will execute fractint and set the initial palette to that in the file
named "chroma.map". In this case "map" is a batch option and "chroma"
is its parameter (or argument).
The reason that these are called "batch" options is because if you are
displaying a fractal image and press the <b> key then a fractint
command line is written to a file named frabatch.bat which contains
all of the options and parameters needed to re-create that fractal.
You can then create it by entering--
frabatch
at the DOS prompt. For example, if you press <b> while the default
M-set fractal is displayed then the contents of frabatch.bat will be:
fractint type=mandel corners=-2.5/1.5/-1.5/1.5
For further information about these batch options, see the
descriptions of "type" and "corners" below.
Many of the options take an argument which is a keyword such as "yes"
or "no". Fractint only uses the first letter of the argument and
ignores the rest, thus you can use either "option=y" or "option=yes"
as you wish. You cannot use spaces on either side of the "=" sign,
thus if you use "option = y" then this will not be interpreted
correctly. You can, if you wish, use ":=" instead of "=", therefore
entering "option:=yes" is okay. The colon is simply ignored.
Page 1
A Guide to Fractint: Part II
Some options take more than one argument and these are separated by
slashes as in "option=one/two/three/four". You can omit arguments
from the right completely (as in "option=one/two/three" in which the
fourth argument is omitted) but if you omit an argument which is not
at the right then you must include its position as indicated by the
slash (as in "option=/one//three/four" in which the second argument is
omitted). Thus, if you want to enter only the fourth argument then
you would use "option=////four".
When you use more than one option they should be separated by one or
more spaces and not by commas or any other punctuation. The entire
command must occur on one line and cannot have carriage returns in it.
You can enter the options on the command line or you can place them in
a file. For example, you can define a file named "set" which contains
the following--
video=SF1 textsafe=y inside=0
and reference it when you execute, thus:
fractint @set
This tells Fractint to obtain the options from a file named "set".
You can name the option file any name you wish. The net result of
executing the command above is that when Fractint comes up it will
display the default M-set immediately without presenting the credits
screen, main menu, or select video modes screens. The VIDEO option
sets the <videomode> to SF1. The TEXTSAFE option suppresses the
credits screen and prevents Fractint from flickering when it first
comes up (it does this while it is checking your video board). This
option should only be used after you know that Fractint runs properly
on your computer. The INSIDE option sets the default inside color to
black which it should be by system default, but isn't.
If you regularly use more than one video mode then you can define
several option files, for example:
fractint @ega
fractint @vga256
fractint @vga16
Page 2
A Guide to Fractint: Part II
and so forth. Each of these defines a different <videomode> and
associated options. There are many, many other possibilities. For
example, you can define an option file so that Fractint automatically
comes up using the small window rather than the fullscreen window.
You can set which colors you want on the Main Menu (and all of the
parameters boxes, etc.) with the TEXTCOLORS option. Command files
cannot be nested.
However, you can have reference to more than one option file on the
command line and you can mix it with other options, for example:
fractint @set type=julia @colors
Page 3
A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ADAPTER=c|e|m
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Normally, Fractint detects which kind of video board you have in your
system automatically as it comes up. In rare instances this auto-
detection procedure does not operate correctly. If Fractint will not
come up at all on your system you could try using this option.
The meaning of the argument is:
c = cga
e = ega
m = mcga
The default is a VGA adapter. There is no "v" argument--if you have a
VGA monitor then you can indicate this by not using this option.
This option should only be used if you are having problems with
Fractint's auto-detection of your video type. For example, your
system may hangup when you first start Fractint.
This option can only be set when executing Fractint--it cannot be
changed from within the program.
Note that when you use the ADAPTER option you may not be able to use
the very highest resolution modes supported by that adapter.
If using the ADAPTER option does indeed solve the problem and Fractint
comes up normally then you should put the ADAPTER statement in a file
named SSTOOLS.INI. For details, see the alphabetic entry under
SSTOOLS.INI in this manual.
Page 4
A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
AMBIENT=nnn (0 - 100)
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used when making fractal landscapes. It alters the
amount of contrast in the image by changing the depths of the shadows
when using the FULLCOLOR and LIGHTSOURCE options.
This option is used to control the degree of ambient lighting in full
color landscapes which are created as Targa-24 files. Unless you have
a Targa board you must convert the output file to a GIF file before
viewing it. This cannot be done by Fractint. The PICLAB program can
convert a .TGA (Targa file) to a .GIF (Graphics Interchange Format)
file.
PICLAB (by Lee Crocker) is 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 to GIF files.
From within PICLAB, the commands to convert from a .TGA to a .GIF file
are:
SET PALETTE 256
SET CREZ 8
TLOAD yourfile.tga
MAKEPAL
MAP
GSAVE yourfile.gif
EXIT
A value of AMBIENT=0 disables this feature. Values from 1 to 100
lower the amount of contrast, thus 100 is the lowest possible
contrast.
If you are using the LIGHTSOURCE option to define the direction from
which light is being cast upon your landscape and the result looks
like the surface of the moon (i.e. it is monochrome and has very dark
shadows) then you can correct for this with the AMBIENT option.
Page 5
A Guide to Fractint: Part II
The AMBIENT option defines the intensity of light from the
lightsource, a value of 0 is the most intense and causes the blackest
shadows and a value of 100 is least intense and causes the weakest
shadows.
You can set this option while Fractint is running. First, press the
<3> key to get the Select File for 3D Transform list. Or,
alternatively you can select this choice from the Main Menu. On the
list, select a file to be displayed in 3D and press <Enter>. You will
get the Select Video Modes screen. Usually you would simply press
<Enter> unless you want to change the mode--the one displayed is the
one the file was saved in.
You will next get the 3D Mode Selection menu. Press <Enter> and you
will get the Select 3D Fill Type screen. Move down to the bottom of
the list of options and select one or both of:
light source before tranformation
light source after transformation
and press <Enter>. You will get a screen on which you are requested
to enter the name of the MAP file to be used. If you want to use the
same map as the source image file used then simply press <Enter>. You
will then get the Planar 3D Parameters screen. Press <Enter> and you
will get the Light Source Parameters screen.
On the Light Source Parameters screen, move the highlight down to the
item which is--
Ambient Light (0-100, '0' = 'black' shadows)
The default value is 20. To change it, overwrite the default value
and press <Enter>. The screen will go completely black and the disk
light will blink. After a short delay the image will begin to be
painted on the screen.
The image you see on the screen represents the amount of light being
reflected by each point in the image, 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.
By default, the Targa-24 created has the name light001.tga. This
filename increments to light002.tga if you create another Targa file.
A file with an extension of .tga is called a lightfile. You can
change the root name of the lightfile with the LIGHTNAME option.
If you have a Targa-24 video board then you can view the lightfile by
recalling it the same way you would a .GIF file.
See also: FULLCOLOR, RANDOMIZE, MAP, 3D, FILLTYPE
Page 6
A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ASKVIDEO=y|n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
If you set ASKVIDEO=n this eliminates the prompt asking you if a file
to be restored is OK for your video hardware. The default is yes.
If all of the fractal images files you restore are those which you
created yourself then you really don't need Fractint to bring up the
Select Video Modes screen for confirmation that the videomode is okay
for your computer so you can suppress this.
Do not set this option to NO if there is any chance that you could try
to bring up an image which has a resolution too high for your computer
to handle. This could happen if you try to display a regular GIF
picture (which, perhaps, you downloaded from a BBS or CompuServe)
without being positive of its resolution. You also might have
problems if you have two monitors and create images for both.
If you place an ASKVIDEO=n option in a command file then you should
probably delete it when first trying out a new version of Fractint
until you are sure everything is okay. This is particularly true if
you are using one of the SVGA modes. In some cases the meanings of
the videomodes may change between Fractint versions. Thus, an image
could be stored as (for example) videomode CF6 but with a new version
of Fractint the CF6 videomode calls for a higher resolution than
before. This isn't common, but it does occur. Thus, it is safest to
temporarily remove this option from your command files when first
using a new version.
If you have a CGA monitor (or a Hercules 2-color monochrome monitor)
then it is now possible for you to make 3D projection images. Invoke
Fractint, making sure you have set ASKVIDEO=y. 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 the description of the BATCH option 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.
This option can only be set when executing Fractint--it cannot be
changed from within the program.
See also: VIDEO
Page 7
A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
BAILOUT=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The BAILOUT option has no effect on regular fractals. However, when
you use the decomposition option (DECOMP) then it has a rather strong
effect on the result. Try bringing up the default M-set and pressing
the <x> key. Enter 128 as the Decomposition value. Return and re-
generate the image. It will be quite different. This is with the
default Bailout Value of 4. Changing the Bailout Value can change the
resulting fractal image considerably.
You can only decompose fractals of the Mandelbrot and Julia families
of fractal types.
You cannot change the Bailout Value by itself from within Fractint (as
you could in Version 14.0). You must exit back to DOS and re-execute
Fractint using the BAILOUT=nnn option to change this value. On the
<y> screen there is a field named Bailout Value but changing it alone
has no effect--you must also change the Potential Value and the result
of doing this not what you want.
When you set the BAILOUT option you are overriding the default bailout
value which Fractint automatically sets for each fractal type. For
fractals computed using integer arithmetic the bailout value may be
between 1 and 127 (if you enter a higher value it then 127 will be
used). For fractals computed using floating point then the bailout
value can be between 1 and 256. On the command line, Fractint will
accept bailout values from 4 to 32000.
You can change the Bailout Value on the <x> screen and would probably
do it far more frequently that way than using the execution option.
Fractals are computed iteratively. In the most simplistic terms, the
computation is
z1 = f(x)
this produces a result which is z1. The formula is then calculated
again, using z1 as input and producing z2 as the result. Z2 is then
used to create z3 etc.
Page 8
A Guide to Fractint: Part II
Thus, iterations two through five are:
z2 = f(z1)
z3 = f(z2)
z4 = f(z3)
z5 = f(z4)
and so forth. Obviously, the number of iterations could go on for
infinity (at least mathematically, in practice computers do not handle
infinite numbers well). Therefore, a method is needed to determine
when to stop iterating. Actually, several methods are used. One is
to count the number of iterations. When n iterations have occurred
then the final result has been achieved. The other method is to
examine the value of the output--when it exceeds some numeric value
then iteration also stops. In either case, a fixed number of
iterations of the formula are performed. The last iteration is the
FIV (Final Iteration Value). For the example above, the FIV is 5.
Iteration is also stopped whenever the calculation becomes a periodic
loop.
The FIV is used to determine what color to assign the pixel for which
the calculation was performed.
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.
For the Mandelbrot fractal the formula which is iterated is (written
in the same style as above) is:
z1 = sqr(z0) + z0
Written in the style which Fractint understands internally, this
formula is:
Mandelbrot(XAXIS) { z = Pixel: z = sqr(z) + pixel, |z| <= 4 }
Here, the 4 is the Bailout Value. Thus, whenever the value of the z
created during the last iteration is greater than 4 then iteration
stops and the last iteration value becomes the FIV and determines the
color of the pixel at that point. This implies that any iteration of
the formula which produces a value greater than the Bailout Value has
the same color.
Page 9
A Guide to Fractint: Part II
Therefore, changing the Bailout Value will change the colors which are
assigned to each point in the fractal being generated. For some
fractal types this can have a major effect on the appearance of the
fractal image.
If you are also using the DECOMP option then setting the Bailout Value
higher will produce a more accurate plot. For a Mandelbrot or Julia
fractal which is decomposed, the Bailout Value should be set to 50 or
higher for the best results. However, the higher you set the Bailout
Value the longer it takes to compute the fractal.
In computing a decomposed fractal, Fractint performs a number of
iterations equal to the Bailout Value and then assigns a color
according to where the actual final value falls on the complex plane.
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. The term "escape-time algorithm" is a fancy way of
saying the method used to determine when to stop iterating the
formula. The term "orbit" is explained in the description of the
INITORBIT option.
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:
either the real OR the imaginary component
is LESS than the bailout value
then the pixel is set to the "biomorph" color. In the formulas given
above the value "z" is a complex number. As such, it has both a real
and an imaginary component, both of which are compared to the Bailout
Value to determine the color to assign to the current pixel position.
When creating biomorphs, effect is a bit better with higher bailout
values: the bailout is automatically set to 100 when the BIOMORPH
option is used. You can try other bailout values with the BAILOUT
option.
Most fractal types have both a fast integer math and a floating point
version. The faster (but sometimes less accurate) integer version is
the default. If you have an 80486 (or a very fast 80386) machine with
a math coprocessor and you are using the POTENTIAL option then you
should set the Bailout Value high. If you try this with a slower
machine you may be waiting until the fat lady sings before getting any
results. Note that when you use the POTENTIAL option that one of its
arguments is the Bailout Value to use, so you do not have to set it
with the BAILOUT option.
See also: POTENTIAL, INITORBIT, BIOMORPH, DECOMP
Page 10
A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
BATCH=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used when you are creating a fractal which takes a very
long time to develop.
It can also be used to convert a file from a 2D image to a 3D image;
to change the video mode of a file; to produce a .GIF file from a
.FRA files, and otherwise act as a filter.
One advantage is that Fractint can automatically make periodic saves
of the developing image so that even if the power is lost only a small
amount of development time is lost. For example, you can save every
30 minutes and therefore cannot lose more than this amount of time.
Usually, when creating a slow fractal you would start it running late
at night and let it cook while you are asleep (or otherwise occupied).
Thus, you could lose up to eight hours worth of fractal should a
mishap occur.
Another advantage is that the fractal is automatically saved whenever
any key is struck and Fractint returns to DOS. This can be useful if
there is the possibility that someone other than yourself may be the
next person at the keyboard.
When the fractal has finished developing, Fractint automatically saves
it and returns to DOS.
If you enter a command such as the following at the DOS prompt:
fractint myfract batch=y
then Fractint will display the image in myfract.gif. If the fractal
is incomplete then it will continue development automatically.
The next time any key is pressed then the current image will be saved
and you will be returned directly back to DOS.
Page 11
A Guide to Fractint: Part II
By default, the image will be saved into a file named fract001.gif.
Actually, it will go into fractnnn.gif where nnn is the next
available, unused number. Therefore, if fract001.gif already exists
then fract002.gif will be used. You can specify a different name to
be used to save the file under, for example:
fractint myfract savename=newfract batch=y
and now the file newfract.gif will be written when any key is pressed.
You can also save to no file whatsoever with:
fractint myfract savename=nul batch=y
When the next key is pressed and the file is saved it will be written
to the special DOS device named nul which is a null device. Therefore
nothing is saved to disk.
Assuming that you recall a partial image which takes a long time to
develop, you can specify that automatic saves be performed at regular
intervals, thus:
fractint myfract savetime=30 batch=y
This will automatically save the file to fract001 every 30 minutes.
The same filename will be used over and over again. If you also
specify the filename, as in:
fractint myfract savename=newname savetime=60 batch=y
then the save will be to the newname.gif file every 60 minutes.
You can also enter other parameters on the command line, for example:
fractint myfract 3d=y savename=newname batch=y
This will save a 3D image of myfract.gif in a file named newname.gif.
If you have any .FRA files created by earlier versions of Fractint you
can convert them as follows:
fractint fractal.fra savename=fractal.gif batch=y
Technically, you can also use batch=n but since this is the default
and is essentially meaningingless, there is no need to do this.
See also: BATCH=config, SAVENAME, SAVETIME
Page 12
A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
BATCH=config
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
If you run Fractint with this option, as in:
fractint batch=config
then the only thing which will happen is that the hard disk light will
go on for a few seconds and then you will return to the DOS prompt.
All that Fractint has done is to create a file named "fractint.cfg".
The content of the file is quite similar to the table you see when you
are on the Select Video Modes screen.
Once the fractint.cfg file exists then Fractint will use it to obtain
the list of video modes rather than its internal version of the table
of video modes. The file can be anywhere in your path and it will be
found.
You can edit the fractint.cfg file so that the list shown on the
Select Video Modes screen contains only those videomodes which your
system is capable of using (or only those you wish to use). You can
assign specific videomodes to the <PFn> keys. You can change the
default videomode.
One reason to create the configuration file and edit it is to remove
all of the entries which are of no use to you whatsoever. Thus,
unless you have a TARGA board then all of the TARGA entries are
meaningless. If you have a 256K VGA system then all of the SVGA video
modes are not usable. Another reason to edit it is to create an entry
for a new video mode.
If you edit the configuration file (using any ASCII editor) and insert
either a <tab> or a <space> at the first position on a line then
Fractint will not include that line when the Select Video Modes screen
is displayed within Fractint. You can also simply delete video mode
lines which are irrelevant on your system.
Doing this can cut down the list of video modes down to the half dozen
or so which you might actually use. In practice, most people probably
never use more than 2-3 different video modes.
Page 13
A Guide to Fractint: Part II
Fractint assigns the first active videomode in the config file to the
<F2> key. Here, "active" means a line which has not been disabled by
having a blank or tab in the first position. The next videomode is
assigned to the <F3> key, and so forth. After <F9> has been assigned
then the next videomodes are assigned to <Shift>-<F1> through <Shift>-
<F9>, and so forth.
Thus, the association of a videomode with a function key is determined
by the position of the active videomodes in the configuration file.
If you take the videomode which you use most frequently and move it so
that it is the second active videomode in the config file then it will
be associated with the <F3> key. When the Select Video Modes screen
comes up the highlight is on the <F3> position by default, thus you
need only press <Enter> to select this mode.
Note that if you edit the config file you may also need to modify your
batch option file, if you have one. For example, if you use a batch
option file named "set" which contains the following:
video=SF1 textsafe=y inside=0 askvideo=n
so that when you execute Fractint with the command--
fractint @set
then the videomode associated with the <Shift>-<F1> key will be used.
If you edit the config file so that this mode has been moved to the
second active line then you should alter your options file so that it
is now:
video=F3 textsafe=y inside=0 askvideo=n
This has exactly the same effect assuming that the videomode which was
at the ninth position in the file (and therefore associated with
<Shift>-<F1>) is moved to the second position and is now associated
with the <F3> key.
The following shows the first few lines of the default configuration
file, as it is produced after you initially create it by using the
batch=config option:
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A Guide to Fractint: Part II
Full FRACTINT.CFG File, built by a 'fractint batch=config' command
name of adapter/mode | AX | BX | CX | DX |mode| x | y |clrs| cmt
======================================================================
IBM 16-Color EGA , 10, 0, 0, 0, 2, 640, 350, 16, cmt1
IBM 256-Color VGA/MCGA , 13, 0, 0, 0, 3, 320, 200, 256, cmt2
IBM 16-Color VGA , 12, 0, 0, 0, 2, 640, 480, 16, cmt3
IBM 4-Color CGA , 4, 0, 0, 0, 13, 320, 200, 4, cmt4
comment1 = Standard EGA hi-res mode
comment2 = Quick and LOTS of colors
comment3 = Nice high resolution
comment4 = (Ugh - Yuck - Bleah)
This display has been modified slightly. In the fractint.cfg file
each of the videomode lines ends with a descriptive comment. There is
not room for the comment in this text so they are given on a separate
line. Thus, "cmt1" means that "comment1" goes here and so forth.
The meanings of the columns of this table are:
---------------------------------------------------------------------
name of adapter/mode
This is a text description. Maximum of 25 characterers.
Leading blanks are not allowed.
---------------------------------------------------------------------
AX
BX
CX
DX
These four are the contents of these four hardware registers at
the time that the INT 10H interrupt is called.
The values entered in these fields must be in hexadecimal.
The default entries for the IBM VGA entries labeled "tweaked"
and "non standard" have AX = BX = CX = 0, and DX = some other
number. Those are special flags to custom-program the VGA
adapter, and are NOT undocumented BIOS calls. Maybe they should
be, but they aren't.
---------------------------------------------------------------------
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---------------------------------------------------------------------
mode
This is a special code which specifies how to write to video
memory. The codes are:
1 Use the BIOS (INT 10H, AH=12/13, AL=color) See Note 1
2 Pretend it's a (perhaps super-res) EGA/VGA
3 Pretend it's an MCGA
4 SuperVGA 256-Color mode for Tseng Labs chipset
5 SuperVGA 256-Color mode for Paradise chipset
6 SuperVGA 256-Color mode for Video-7 chipset
7 Non-Standard IBM VGA 360 x 480 x 256-Color mode
8 SuperVGA 1024x768x16 mode for 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 for Trident chipset
16 SuperVGA 256-Color mode for Chips & Tech chipset
17 SuperVGA 256-Color mode for ATI VGA Wonder chipset
18 SuperVGA 256-Color mode for EVEREX chipset
19 Roll-your-own video mode (defined in YOURVID.C)
20 SuperVGA 1024x768x16 mode for ATI VGA Wonder chipset
21 SuperVGA 1024x768x16 mode for Tseng Labs chipset
22 SuperVGA 1024x768x16 mode for Trident chipset
23 SuperVGA 1024x768x16 mode for Video 7 chipset
24 SuperVGA 1024x768x16 mode for Paradise chipset
25 SuperVGA 1024x768x16 mode for Chips & Tech chipset
26 SuperVGA 1024x768x16 mode for Everex Chipset
27 SuperVGA Auto-Detect mode (look for your adapter)
28 VESA modes
Note: 1 Very slow
--------------------------------------------------------------------
x
y
x = number of pixels across the screen
y = number of pixels down the screen
Both of these must be in the range from 160 to 2,048 pixels.
--------------------------------------------------------------------
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---------------------------------------------------------------------
cls
The number of available colors (2, 4, 16, or 256).
---------------------------------------------------------------------
cmt
Text comment about the mode. Maximum of 25 characters. Leading
blanks are allowed. Humor is verboten.
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 Shift/Control/Alt
variants, and many Alt-x keypad combos) when the program is running.
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 Fractint source file contains a program called "yourvid.c" which
is the skeleton around which you can build a custom video mode. For
further details, see the comments within that file.
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.
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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.
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.
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A Guide to Fractint: Part II
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 option, 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 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 your config.sys file to
reduce 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.
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A Guide to Fractint: Part II
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 window edges)
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).
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A Guide to Fractint: Part II
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) have been successfully tested.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
BIOMORPH=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The "nnn" of BIOMORPH=nnn is the number of a color from 0 to 255. If
this value is -1 then the biomorph option is turned off (this is the
default). Setting BIOMORPH=0 (i.e. to black) generally works best.
The BIOMORPH option causes the appearance of vaguely biological,
amoeboid shapes to appear in Mandelbrot or Julia fractals. The only
real way to understand what this option does is to try it, thus:
fractint biomorph=0
may be entered from the command line or you can press <x> and change
the value for the biomorph option from -1 to 0 on the options screen.
The resulting Mandelbrot set will look quite different. It is well
worthwhile to set this option on occasionally since the results are
almost always very interesting and fun to explore. Also try the
combination:
fractint biomorph=0 type=julia
since the biomorph form of the full Julia set is delightful.
These types have been explored extensively by Clifford A. Pickover, of
the IBM Thomas J. Watson Research center. Thus, you can not only have
fun but be in good company doing so.
As implemented in Fractint, biomorph fractals are regular
Mandelbrot/Julia set pairs that may be plotted with or without the
"biomorph" option Pickover used to create organic-looking beasties.
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.
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A Guide to Fractint: Part II
Try:
fractint type=manfn+zsqrd biomorph=0 corners=-8/8/-6/6 function=sin
to see big biomorphs gobbling up little biomorphs.
The idea behind biomorphs 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 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.
When you toggle from the Mandelbrot set to the corresponding Julia set
with the <space> key, the default corners on the Julia are three times
bigger than those on the Mandelbrot so that all of the biomorph
appendages are visible.
The BIOMORPH option works with most Mandelbrot and Julia fractal
types, but not all. In particular, it does not work with the Mandelfn
type.
Biomorph fractals work very well on monochrome monitors. If you have
a mono system, try the Marksmandel (and Marksjulia) types with
BIOMORPH turned on. If you have a color monitor, you can obtain a
gray scale palette by pressing the <F2> key while the Palette Editor
box is displayed.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
BRIGHT=nn/nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The nn/nn arguments of this option are the Blue:Red ratio.
This ratio is used only when viewing blue/red 3D images through
blue/red glasses. The technical term for these glasses is "funny
glasses". You probably have a pair lying around your house from the
last time you saw a 3D movie at the theatre. If you do not then you
could have a pair you obtained to watch a 3D television commerical for
a popular soft drink. If, after searching through your belongings
carefully you find that you cannot locate yours then you can make a
pair. Trying to buy a pair in a store is almost impossible. No, make
that *is* impossible.
To make a pair of funny glasses, go to a stationery store and buy a
set of report covers in blue and red mylar. Apply a pair of scissors
to the report covers in a suitable manner and tape or glue the lenses
between two pieces of cardboard from which holes have been cut out.
Cut the cardboard sandwich into the shape of eyeglasses and voila! you
are ready for 3D viewing of fractals.
The human eye is not equally sensitive to both blue and red. In
addition, adjustments may be needed for the exact shades of blue and
red of the lenses of your funny glasses. Also, if you are using
purchased red/blue glasses they are usually colored for the reflective
light of a printed image and not the light generated by a CRT.
If the image appears to reddish then raise the blue/red ratio; if is
too blue then lower the blue/red ratio. When you get the ratio right
then the image should be gray.
Similarly, if you get red ghost lines then you can counter this by
altering the BRIGHT ratio.
You should use the GLASSES1.MAP palette when viewing 3D fractals.
Usually this map is loaded for you automatically by Fractint.
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A Guide to Fractint: Part II
The BRIGHT option can be set from within Fractint. First press <i> to
get the IFS and 3D parameters box. Set the STEREO option to 1 or 2
and press <Enter>. You will get the Funny Glasses Parameters box.
Move the highlight down to the Red Brightness Factor line to set the
red percentage. The next line is the Blue Brightness Factor. The
default for red is 80% and the default for blue is 100%.
One reasonable constellation of options to try is:
BRIGHT = 100% / 100%
CONVERGE = -5
INTEROCULAR = 5
These settings produce a pretty good 3D image even without the funny
glasses.
See also: 3D, IFS, STEREO, CONVERGENCE, CROP, MAP
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
CENTER-MAG=Xctr/Yctr/Mag
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option has a rather specialized use.
Normally, when you press the <b> key from within Fractint then a line
is appended to the frabatch.bat file which contains the command and
options required to generate the fractal currently displayed. This
line contains the option CORNERS= which gives the coordinates of the
four corners of the fractal. If you use the CENTER-MAG option with no
arguments then instead of writing CORNERS= to frabatch.bat, Fractint
will write the location of the center of the fractal and a
magnifification value.
Some other fractal programs (and some publications) require the center
coordinate and magnification rather than the corner coordinates. If
you are not using such a program or writing for such a publication
then this option is of no use to you unless you know the X,Y
coordinates of a point you wish to view.
In any case, the <tab> display shows the coordinates of the center
point of the image.
The center point and magnification values will not be correct if you
have altered the aspect ratio of the image from the default 1.33333.
Thus, it will not be correct if you changed the shape of the zoom box
when creating the fractal, or rotated it.
See also: INVERT, CORNERS
Inversion of a fractal is performed around the center point.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
COMPORT=port/baud/options
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used to define the parameters used by a serial printer
port. It may be used as an override to the parameters set within DOS
by the MODE command. If the DOS parameters are okay then you don't
need this option.
The arguments are:
Port = 1, 2, 3
Baud = 115, 150, 300, 600, 1200, 2400, 4800, 9600
Options: 7, 8 | 1,2 | e,n,o
The options may appear in any order. The 7 or 8 specifies the number
of data bits in each byte. The 1 or 2 specifies the number of stop
bits used. The parity is e=even, o=odd, or n=none.
Example: comport=1/9600/n81
This sets the serial communication port COM1 to 9600 Baud, no parity,
8 bits per character, 1 stop bit.
This option cannot be set from within Fractint.
If you use the COMPORT option, you must use it every time you use
Fractint to print an image, so you should probably place it in an
options file.
See also: PRINTER
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
CONVERGE=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This is a funny glasses parameter used only with red/blue stereo 3D
images. The nn argument is the percentage of the screen.
When a stereo image is viewed correctly it floats in space. It can
appear to float out in front of the screen or way back inside.
Changing this option causes it to move from outside to inside or vice
versa. Neophyte stereophiles tend to like outside floaters and
advanced stereophiles tend to like inside floaters.
A higher value moves it outside; a lower value inside.
This option interacts with the INTEROCULAR option, so it will take
some fiddling to get it right.
A stereo image is created by superimposing a blue image and a red
image in the same space but slightly offset from each other. The
CONVERGE option controls the degree of separation between the red and
blue images.
This option is more likely to be set from within Fractint than on the
command line. To set it, first press the <i> key to get the IFS and
3D Parameters box. Select the 3D Transform Parameters menu choice and
press <Enter>. This choice is the default when you bring up this box.
Set the STEREO option to 2 or 3 and press <Enter>. You will get the
Funny Glasses Parameters box. Move the highlight down to the line--
Convergence adjustment (positive=spread greater)
and enter a new value. The default value is zero.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
CORNERS=xmin/xmax/ymin/ymax[/x3rd/y3rd]
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
These are the four corner coordinates of a 2D image or the six
coordinates of a rotated or distorted parallelogram.
On the default full Mandelbrot fractal, the Y-axis has a low value of
-1.5 and a high value of +1.5. Thus, the zero line is halfway up the
y-axis.
The x-axis has a low value of -2.5 and a high value of +1.5. Thus,
the zero line is somewhat to the right of halfway across the x-axis.
Within Fractint, three systems of geometric location exist. The first
two are variants of each other and are based upon the locations of the
four corners of the image. These locations are displayed on the <tab>
key and also obtained when you press the <b> key. However, the method
of specifying the coordinates differs between the <x> and <b> keys.
The third method is by specifying the location of the center of the
image and the degree of magnification. This information is also
displayed on the <tab> key and is obtainable with <b> (provided that
Fractint is executed with the CENTER-MAG option).
The display produced by the <tab> key has a table such as the
following:
CORNERS X Y
Top left -2.5 1.5
Bottom right 1.5 -1.5
Top left A B
Bottom right C D
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A Guide to Fractint: Part II
(-2.5,1.5) ==========================
A B = =
= =
= =
= =
= =
= =
= =
= =
========================== (1.5,-1.5)
C D
This is for the full mandelbrot. For the full Julia fractal the
coordinates are different:
CORNERS X Y
Top left -2.0 1.5
Bottom right 2.0 -1.5
since the X-axis runs from -2.0 to +2.0 in Julias--therefore the zero
line is exactly halfway across the x-axis. The image is centered on
the (0,0) location. Similar to Mandelbrot fractals, the Y-axis runs
from -1.5 to +1.5.
When you press the <b> key then the CORNERS= option values for the
current image are written to the frabatch.bat file.
For the full M-set, the result is:
CORNERS=-2.5/1.5/-1.5/1.5
A B C D
D 1.5 ==========================
= =
= =
= =
= =
= =
= =
= =
= =
C -1.5 ==========================
-2.5 1.5
A B
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A Guide to Fractint: Part II
This is in the order:
CORNERS= X(min)/ X(max)/Y(min)/Y(max)
The top left corner is (X(min), Y(max)) and the bottom right corner is
at (X(max), Y(min)).
The full CORNERS= syntax is:
CORNERS=xmin/xmax/ymin/ymax[/x3rd/y3rd]
The x3rd argument is the location of the bottom-left corner of a
rotated or stretched parallelogram. If you are displaying a 3D
fractal and press the <b> key the x3rd and y3rd values are not written
to the frabatch file. They appear when a 2D image is stretched or
rotated. They are also not displayed on the <tab> display (except,
again, for stretched or rotated 2D images). These values may be set
be being passed as command option arguments.
After you press <b> to append a fractint statement to the end of the
frabatch.bat file and exit Fractint, you can usually execute frabatch
by just typing its name at the DOS prompt. However, in some instances
this does not work. Fairly often the fractint statement and all of
the current options on the line within the frabatch file can exceed
120 characters in length. This is the DOS maximum length for a
command line so when you execute frabatch all characters after the
120th are lost and usually the execution fails.
The way around this is to copy frabatch to a file named (for example)
"corners". Edit the corners file so that it contains only the
CORNERS= statement and its arguments. In many cases this argument
will take up many characters because of the number of decimal places.
Then edit the frabatch file and delete the CORNERS= option and replace
it with @CORNERS, which is a call to include the contents of the file
named "corners" at this point. In this manner you can exceed DOS
command line length limit.
You cannot directly set the corner locations for a new fractal from
within Fractint. To accomplish this, use the CORNERS= option when
executing Fractint. You can create a series of images within the same
frabatch file by executing Fractint several times with slightly
varying CORNERS= values each time.
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A Guide to Fractint: Part II
The following diagram shows the location of some of the named areas
within the full Mandelbrot set:
\
\ /
NW Radical North ▄▄▄ NE
Radical
* North . . Radical ┌──▀▀▀──┐ . .
or . . │ │ . .
Seahorse ....┌─┐ └───────┘ ┌─┐...
Valley . └─┘ ┌──────────────────────┐└─┘
. . │ │
.. ▄ * │ │
Big ┌──────┐ │ MAIN │
Midget ┌─┐ │ │ │ BODY │
Spike ──────■────────■│ │ │ Head │ │ ─── East
Topknot └─┘ │ │ │ or │ Valley
└──────┘ │ │
..▀ * │ CARDIOID │
. . │ │
* South . ┌─┐ └──────────────────────┘ ┌─┐
or ....└─┘ ┌───────┐ └─┘...
Elephant . . │ │ . .
Valley . . South └──▄▄▄──┘ . .
SW Radical Radical ▀▀▀ SE
Radical
/ \
/
See also: 3D
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
CROP=nn/nn/nn/nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option trims the edges off stereo (red/blue) pairs.
The nn argument is the percentage of the screen to crop. The
arguments
are in the order:
CROP= lr/rr/lb/rb
in which: lr = left red
rr = right red
lb = left blue
rb = right blue
The default values are 4/0/0/4 percents.
This option helps keep the visible part of the right image the same as
the visible part of the left image. If there is too much in the field
of either eye that the other doesn't see then the stereo effect can be
ruined.
If nothing else you do gets you a good, stable stereo image which
floats in space rather than being on the surface of the CRT, then try
diddling with this option.
The 3D options are very sensitive to human vision. You must
continually tweak the options to improve the result.
Note that this cropping has nothing whatsoever to do with the cropping
of a viewing window option on the <v> screen. It is functionally
similar but is customized for red/blue images.
You can change these values from inside Fractint on the Funny Glasses
Parameters screen. The four fields of interest are:
Left red image crop (% of screen) default: 4%
Right red image crop (% of screen) default: 0%
Left blue image crop (% of screen) default: 0%
Right blue image crop (% of screen) default: 4%
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
CYCLELIMIT=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Sets the speed of color cycling. Technically, the number of DAC
registers updated during a single vertical refresh cycle.
Legal values are 2 - 255, default is 55 for all fractal types except
PLASMA, for which the default is 256.
This value cannot be altered from within Fractint as a value, but the
color-cycling speed may be adjusted with the <up arrow> and <down
arrow> keys.
If you place a CYCLELIMIT option in an option file (such as @SET) then
it has the effect of defining the default speed which occurs when
color-cycling mode is entered.
You can also write a special option file which is customized for the
display of a particular fractal image file. By using this option you
can preset the color-cycling speed. Some fractals look best when the
colors change quite slowly; others like fast changes.
For example, you can create a batch file named pizza.bat which
contains
the following--
fractint pizza3 cyclelimit=250 mapname=army @set
in which "pizza3.gif" is the name of a fractal gif file and in which
the @set file contains:
video=F3 textsafe=y inside=0 askvideo=n
Now when you enter "pizza" at the DOS command line then the image will
be brought up directly (with no credits screen, Main Menu, etc.). All
that is left to do is to press the <c> key to begin color-cycling.
Unfortunately, you can't start color-cycling via any command line
option and so you can't create a self-running fractal.
If you enter an invalid number then it will simply be ignored--you
will
not get any error message.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
DECOMP=2|4|8|16|32|64|128|256
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is fun to play with.
It may be used with any M/J fractal, so try:
fractint decomp=128
when executing Fractint or change it from inside by pressing <x> and
setting the Decomp Option to 128.
This radically changes the way the fractal looks.
If you change the MAXITER value before creating a decomposed fractal
you can also get different results, especially if you lower it to say
3-4. Changing the BAILOUT value also has a signficant effect, even
changing it as little as one whole unit, for example from 12 to 13.
A higher bailout value will give a more accurate plot, at some expense
in speed. You might want to set the bailout value to a higher value
than the default. A value of about 50 is a good compromise for M/J
sets. Actually, at higher bailout values there is a fair bit of
expense of speed.
The argument value (which must be a power of 2 from 1-8) invokes the
corresponding decomposition coloring scheme.
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. This is one coloring
protocol.
Using DECOMP 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.
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If you use 4 as the parameter, points ending up in each quadrant are
given their own color
If you use 2 as the parameter, (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 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.
In terms of a complex plane, the geometry of the M-set is:
\ │ Imaginary
\ / │ Y
-R,+I ▄▄▄ │
+R,+I
. . ┌──▀▀▀──┐ . .
. . │ ││ . .
....┌─┐ └───────┘ ┌─┐...
. └─┘ ┌──────────────────────┐└─┘
. . │ │ │
.. ▄ │ │ │
┌──────┐ │ │ │
Real X ┌─┐ │ │ │ │0 │
────── ──────■────────■│─│ │──────│
│───────────────│─────────────────────────
└─┘ │ │ │ │ │
└──────┘ │ │ │
..▀ │ │ │
. . │ │ │
. ┌─┐ └──────────────────────┘ ┌─┐
....└─┘ ┌───────┐ └─┘...
. . │ ││ . .
. . └──▄▄▄──┘ . .
▀▀▀ │
-R,-I / \ │
+R,-I
/ │
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
DISTEST=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option widens the very thin strands which are part of the inside
and which connect all of the midgets of the M-Set. Instead of hiding
invisibly between pixels, these strands are made one pixel wide. You
can make these strands especially visible by setting the INSIDE color
so it is bright shocking pink or something equally garish.
One practical reason for doing this is if you are preparing a fractal
image for publication or reproduction, especially in black-and-white.
Fractals generally print much better if the strands of inside have
been
fattened up a bit.
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. You should also up MAXITER to 1000.
Normally you would set INSIDE=0 so it is black.
This option may be set from within Fractint with the <x> key. The
field is named Distance Estimator.
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.
Note that fractals usually develop much more slowly when the DISTEST
option is used. Floating point arithmetic should be used.
Actually, since the DISTEST option is most valuable when an image with
many pixels (for example 1600 x 1200 x 2) is being developed to be the
final image used for reproduction, it is more likely to run for days
rather than hours.
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.
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A neat thing to do is to set the DISTEST fairly high and then change
to
a gray scale map like gamma1. As you color-cycle, you get to place
where there is a dramatic shift from white to black. The "unit circle"
that surrounds the M-set, for example, begins to "shrinkwrap" the set.
In fact, what you are seeing is the approximation of the M-set
boundary
by the equipotential curves. These dynamic sequences can present most
of what we know about the M-set. For more about this subject, see
Part
III of this Guide.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
EPSF=1|2|3
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option causes the fractal image to be written in Postscript
format
to a file. The default filename will be fract001.eps.
The argument is a code which determines how "well-behaved" the EPS
file
is. The following is a list of the code numbers and their meanings:
1 means by-the-book Postscript encapsulation
2 allows settransfer and setscreen *
3 is a free-for-all.
* includes code that should make the code still work
without affecting the rest of the non-EPS document.
Normally, printfile output goes to a file named fract001.prn where
"fract001" is the filename. If you use the EPSF option then the
output
will be written to "fract001.eps" but only if the file to which the
output would have been written was "fract001.prn". If you also use
the
PRINTFILE option to change the print filename then the output name may
not be set correctly.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
EXITMODE=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The default is 3, which resets the BIOS videomode to 80x25 color text
mode on exit from Fractint.
The value nn is in hexadecimal. Consult the documentation for your
computer or video graphics board for a list of the BIOS video modes
supported by your computers.
You can also check the documentation for the MODE command in DOS but
it
won't give you the hexadecimal values for each video mode.
The default exit mode is a text mode. You may wish to make it a
graphics mode if you are returning to a graphic environment, such as
Windows.
Fractint does no checking of the value you enter.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FILENAME=name
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
You can execute Fractint with this option--
fractint filename=myfract
but you do not need to enter the name of this option, thus--
fractint myfract
will use the name myfract.gif as the input filename. If you do not
enter a filename on the command line, there is no default.
The filename can be a path--
fractint images\myfract
The filename can be an [older] FRA format file--
fractint myfract.fra
The filename can be a TARGA format file--
fractint myfract.tga
One use for the FILENAME option is for shell programming. Thus, you
can write a batch file (or alias) named, for example, FFD.BAT. It can
contain--
fractint filename=%1 @set @colors
so that you can enter the command line--
ffd myfract
and automatically get the option settings contained in the @set file
and the text colors specified in the @colors file.
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A Guide to Fractint: Part II
You can specify the filename from within Fractint by pressing the <r>
key. A list of the image files in the current directory will be
displayed from which one may be selected. The names of subdirectories
are shown with a \ as the last character.
You may enter a subdirectory by selecting it. A prompt will appear
showing the name of the chosen subdirectory. Press <Enter> to enter
it.
You can also change the name to that of any reachable subdirectory.
Specify the drive character if the subdirectory is not on the current
drive (for example, to read the image in from a floppy). You can also
enter wildcards and all files matched will be displayed. Thus, you
can
enter--
d:\images\fracts*.gif
to obtain a list of all of the files in the images directory on the d
drive which are gif files with names starting with "fracts".
When you are on the Select File to Restore screen (or on the Select
File for 3D Transform) screen and you press any qwerty key, then a
line
will appear just below the file list which prompts--
Search Path for: j
Here the j indicates that the key which you pressed was <j>. Write in
the name of a directory, for example:
Search Path for: ..\images\*.gif
and a list of all of the GIF files in the parallel directory named
"images" will be displayed.
If you omit selection of any files within the directory then the names
of all of the files will be displayed, for example if you enter--
Search Path for: ..\images
then all the filenames in that directory will be displayed. However,
you must be very careful not to press the <Enter> key unless the
highlight is on the name of an image file. Otherwise.....dogmeat.
If you are using an SSTOOLS.INI file and use the FILENAME= option you
cannot omit the option name "FILENAME=" as you can at the command
line.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FILLTYPE=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This selects which kind of fill type method to use when creating a 3D
image.
To select the fill type from within Fractint, press <3> to select a
file for 3D transformation and press <Enter>. You will get the Select
3D Fill Type menu. The following are the fill types:
-1 Surface grid
0 Draw points
1 Connect dots (wire frame)
2 Surface fill (colors interpreted)
3 Surface fill (colors not interpreted)
4 Solid fill
5 Light source before transformation
6 Light source after transformation
The number is the code for the nn argument to the FILLTYPE= option.
After you select a fill type and press <Enter> then you will get a
parameter box which lists 3D parameters you can modify. Usually, this
is a fairly long list.
Using the default M-set, you could select each of these fill types in
turn and view the result. Some people like one way of viewing the 3D
image and some another. To each his own and all that.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FINATTRACT=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The purpose of FINATTRACT is to bring detail out of the lakes of Julia
fractals. It works well with the lambda and magnet fractal types.
In dynamical terms, we say that "Infinity is an Attractor", since 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 set is a single band of one color and is all the
points that are attracted to infinity at the same rate. These sets
(bands of color) are termed "Level Sets" since 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.
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 Julias which have a "lake" (normally colored blue by default)
have
a Finite Attractor within this lake, and the lake turns out to be the
Basin of Attraction of this Attractor.
The FINATTRACT option 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 example, try:
fractint type=lamdafn function=sin
finattract=y
params=.5/.5/0/0
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A Guide to Fractint: Part II
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.
This does not occur for all settings of the parameter, for example the
lake of params=0/1/0/0 stays the standard blue.
The FINATTRACT option does not work for the lakes of Mandelbrot
fractals since every point in a Mandelbrot is, in effect, a single
point from its related Julia fractal. A Mandelbrot's lake has an
infinite number of of points and therefore an infinite number of Julia
sets and therefore an infinite number of finite attractors also.
To find a Julia with a usable lake, zoom on the Mandelbrot to a point
exactly on the edge of its lake. Pick a point where the center of the
zoom box is inside the lake, but not too close to the shoreline and
then press the <spacebar>.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FLOAT=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This turns floating point calculation on.
Floating point is much slower than integer calculation but is also
required for some fractal types and option combinations. You should
have an 80486, or an 80386 with a coprocessor chip, or an awful lot of
patience.
You can turn floating point on with this command line option, or by
pressing the <f> key within Fractint, or by changing this option on
the
<x> list of parameters.
A 3D image may be slow in being restored if it was created with float
arithmetic.
Floating point cannot be used for plasma fractals. This includes any
GIF imported which was not created by Fractint since these are
processed as plasma fractals. The Barnsley IFS/IFS3d types are also
always produced using integer math.
In some cases a complete fractal image may not be a true fractal.
This
can occur when the limitations of integer arithmetic are exceeded.
Changing to floating point will create the correct image.
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.
If you are using the SOUND=x option then you should also turn floating
point on to get better results.
Note that Fractint itself can set this option for you, and will
sometimes do so in the middle of computing a fractal.
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)]
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A Guide to Fractint: Part II
(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), 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.)
Using integer arithmetic, the zoomer you go, the slower goes Fractint.
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.
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A Guide to Fractint: Part II
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FORMULAFILE=formulafilename
FORMULANAME=formulaname
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
If you press <t> while running Fractint you will get a list of fractal
types. If you pick the "formula" entry then a list of all the formula
files in the directory will appear. Fractint comes with one such file
which is named "formula.frm". If you pick this name then a list of
the
formulas within the file will be displayed. If you pick one of the
formulas then a parameter box will come up. After you press <Enter>
then the fractal described by the formula will be created.
You can edit the formula.frm file with any ASCII editor. Despite the
size and complexity of Fractint, at root it is the evaluation of a
single formula repetitively. The formula file contains many examples
of fractal formulas.
Both the FORMULAFILE and FORMULANAME options must be used to create a
formula fractal in batch mode.
If you want to create new formulas, you can either add them to the
fractint.frm file or create a new formula file.
A fractal formula has the following structure:
Formulaname(symmetry) {initial: iteration, bailout}
Formulaname
The "Formulaname" will appear on the list of formulas within the
formula file when the user picks the name of the file from the
list displayed within Fractint. It may also be specified on the
command line.
Typical formulanames are:
Mandelbrot
Dragon
MarksMandelPwr
Newton4
halley
Cubic
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A Guide to Fractint: Part II
The formulaname you assign must be fewer than 16 characters
long.
There is one special formulaname which is "Comment". The
contents of a formula definition with this name will be ignored.
For example:
comment = { Mandelbrot form 1 of the Tetration formula }
A comment may be as long as you wish, for example:
comment = {
FRACTINT.DOC has instructions for adding new
formulas
to this file. Note that there are several
hard-coded
restrictions in the formula interpreter:
1) The fractal name through the open curly
bracket must be on a single line.
2) There is a current hard-coded limit of 30
formulas per formula file.
3) Formulas must currently be less than 200
characters long. Comments may be as long
as needed.
}
You do not actually need the "comment =" part of the formula
definition since it is the default. Thus, text enclosed in
curly
braces will be taken to be a comment. The following is an
example:
{ These formulas were written by Maxwell Honeyhugger }
Symmetry
This specifies whether the fractal image created by the formula
is to be symmetrical. Examples are:
(XAXIS) symmetrical across X-axis
(YAXIS) symmetrical across Y-axis
(XYAXIS) symmetrical across both axes
(ORIGIN) flip image across Y-axis
(PI) purpose of this symmetry not known
none asymmetrical
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A Guide to Fractint: Part II
Examples of the symmetry of some of the formulas from the
fractint.frm file are:
Mandelbrot(XAXIS)
Newton(XYAXIS)
The fractint.frm file does not contain any formulas which are
symmetrical across the Y-axis only. There are no examples in
fractint.frm for the following symmetries:
(YAXIS)
(ORIGIN)
(PI)
You can tell a fractal's symmetry almost as soon as it starts
developing. If it is symmetric in the x-axis then the pixels
will appear on both sides of the screen and build up towards
the
middle. If it is y-axis symmetric then both top and bottom
rows
of developing pixels will appear. If there is no symmetry then
the pixels will develop from the top left corner across and
then
repeat for each row. The symmetry you notice when a fractal
first starts to develop will appear only if the image which is
being created is itself symmetric. Thus, if you are a zoom or
so down in a symmetric fractal, you can select a non-symmetric
shape for enlargement. The pattern of development of the
initial pixel assignments is most clear at the highest level,
before any zooming at all.
Initial Condition
The initial condition follows the left curly brace and
terminates with a colon, thus--
{ initial:
A typical example of an initial condition is--
{ z = Pixel:
Here "z" is a complex number. You can create a new variable by
simply referencing it. All variables are automatically
complex. The name you assign to a variable must begin with an
alphabetic character and may be up to 8 characters long.
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A Guide to Fractint: Part II
Examples of initialization statements are:
1. z = 0:
2. z = (1,1):
3. a = (0,0); b=(0,0):
4. z = P1:
5. z = pixel:
6. z = pixel, c = z ^ (z - 1):
7. z = pixel, c = log(pixel):
8. c = z = 1 / pixel:
9. p = pixel,
test = p1 + 3,
t3 = 3*p,
t2 = p*p,
a = (t2 + 1)/t3,
b = 2*a*a*a + (t2 - 2)/t3,
aa3 = a*a*3,
z = 0 - a :
#1 In example #1 a complex variable named "z" is declared and
initialized to zero. Traditionally, "z" is used as the name of
the value which is iterated. It starts at one value and
increases slightly with each iteration until it reaches its
final value. Since z is a complex number, it has two parts
which
are the real part and the imaginary part. In this example, both
parts are initialized to zero. Thus, when iteration starts z
will have a value of (0,0). This means that iteration will
start
at the point near (for M-set) or at (for J-set) the middle of
the complex space. It starts where the zero values for the
x-axis and y-axis meet.
The initial value is referred to as z(0). It may also be set by
the user at execution time with the INITORBIT option. The two
parts of z(0) are sometimes referred to as:
Real perturbation of Z(0)
Imaginary perturbation of Z(0)
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A Guide to Fractint: Part II
The point is that z(0) is a complex number with a value of (R,I)
where R is real and I is imaginary.
#2 In example #2, the real and imaginary parts of z are initialized
separately. Since both parts are here the same this could have
also been written as z=1:. Or, the two parts could have
different initial values, as in--
z = (1,0):
#3 The third example is the same as the first except that two
variables are initialized. Statements within the initialization
section are separated by semi-colons (;). Statements may be on
the same line or not, as you wish. Thus, you can write--
a = (0,0);
b = (.5,1):
#4 Example #4 also shows the declaration and initialization of a
variable--
z = P1:
Here the value "P1" has a special meaning. Many fractals have
a set of four parameters which may be set. Usually when you
select a fractal type and press <Enter> a parameter box will
appear in which Parameters 1 through 4 may be accepted or
changed. Thus, P1 refers to the first Parameter. The default
value is commonly zero but may be changed in the Parameter Box.
Changing the value of P1 can have strong effect on the
appearance of the fractal.
When the initialization statement is z=P1: this can mean that
the person creating a fractal image may select the starting
value for z, at least for the AltJTet formula. For other
formulas the use of P1 is different. In some it is used to
define the end condition; in others it is used in the
calculation itself. For further details, see the description
of the PARAMS option.
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#5 Similarly to above, the initiazation statement--
z = pixel:
has a special meaning. The name "pixel" refers to the current
screen location. This location is not determined using the
(X,Y) locations described above for the CORNERS option and the
<tab> key display. Instead, the screen locations are the
coordinates of the current screen pixel in complex space. The
native space of fractals is complex space. Locations within
this space are specified by a complex number, which is the
value named "pixel".
This sets the initial value for the start of the iterations to
the location of the pixel at the upperleft corner of the
screen.
If the image being created is the result of a zoom then these
coordinates will be different for each zoom level down. In
effect, the location of "pixel" is the complex coordinates of
the upperleft corner of the zoom box.
A map of the complex space of the full M-set is:
\ │ Imaginary
\ / │ Y
-R,+I ▄▄▄ │
+R,+I
. . ┌──▀▀▀──┐ . .
. . │ ││ . .
....┌─┐ └───────┘ ┌─┐...
. └─┘ ┌──────────────────────┐└─┘
. . │ │ │
.. ▄ │ │ │
┌──────┐ │ │ │
Real X ┌─┐ │ │ │ │0 │
────── ──────■────────■│─│ │──────│
│───────────────│─────────────────────────
└─┘ │ │ │ │ │
└──────┘ │ │ │
..▀ │ │ │
. . │ │ │
. ┌─┐ └──────────────────────┘ ┌─┐
....└─┘ ┌───────┐ └─┘...
. . │ ││ . .
. . └──▄▄▄──┘ . .
▀▀▀ │
-R,-I / \ │
+R,-I
/ │
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Thus the initial value of pixel is in the second quadrang at
location (-R,+I) in which "R" is the real part and "I" the
imaginary. The x-axis is a real number and the y-axis is an
imaginary number.
The "pixel" value (i.e. the location of the last pixel) may be
used also in the computation or in defining the end condition.
Fractal types for which the initial value of z is "pixel" are--
Mandelbrot
Dragon
MarksMandelPwr
DeltaLog
Newton4
and several others. The formulas for MTet and AltMtet are
identical except that for the first the initialization is
z = pixel: whereas for the second it is z = 0:
#6 The sixth example of an initialization statement is--
z = pixel, c = z ^ (z - 1):
First of all, notice that there is a comma between the
definitions of z and c, not a semi-colon. These are parts
of one statement, not two statements.
The variable "c" is also a special one. It is a coefficient
and
is a complex value. For Julia fractals it is a constant value.
For Mandelbrots it is defined within the formula and
therefore varies. The user can also set the value of c at the
time of execution or when beginning creation of a fractal. For
details see the description of the PARAMS option. The first
two
parameter values are the real and imaginary values of the
number
to which c will be set.
The Mandelbrot set is a composite of all the Julia sets.
First, find the screen pixel at the center of each Julia set in
the Mandelbrot set.
Next, plot it at the screen coordinate corresponding to the
value of c. This produces the Mandelbrot set.
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In the statement above, the c location is intialized to be--
c = z ^ (z - 1)
Thus, c is computed to be the value of z raised to the power of
z-1. This defines the relationship between a Mandelbrot
fractal
and its corresponding Julia fractal. It determines the
appearance of the Julia associated with a point on the M-set.
c=cos(z)
The location c may bear a mathematical relationship to the
value
of z. Z is the location of a point in the Mandelbrot set.
This
defines the transformation of the M-set to get the J-set.
Other mathematical functions which may be used are:
abs() -- absolute value
conj() -- conjugate value
* cos() -- cosine
* cosh() -- hyperbolic cosine
* exp() -- exponential
imag() -- imaginary
* log() -- logarithm
real() -- real
* sin() -- sine
* sinh() -- hyperbolic sine
* sqr() -- square root
Asterisked functions are part of the set named "fn". Thus fn
may
be any of the following functions: cos, cosh, sin, sinh, sqr,
log, or exp.
On the list of fractal types produced with the <t> key are a
number which have "fn" as part of the type name. Each of these
is a set of fractal types. For example, the type "LambdaFn"
consists of LambdaCos, LamdaCosh, LamdaSin, etc. The definition
of each of these types could be identical except for one
statement. For example,
z = fn(z)
corresponds to--
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z = cos(z)
z = cosh(z)
z = sin(z)
and so forth for each of the functions in the set fn. The term
fn is not one you can use when defining a formula--you must use
the name of a function within the set.
#7 The seventh example is--
c = z = 1 / pixel:
This demonstrates how to assign the same value to more than one
destination. Both c (the coefficient) and z (the location) are
set equal to the reciprocal of the location of the last pixel.
#8 The next example should be easy to understand at this point--
z = pixel, c = log(pixel):
#9 Since the meaning of the last example was easy, let's attack
a more complex initialization, such as--
t1 = pixel * pixel
t2 = 3 * pixel
a = (t1 + 1)/t2,
z = 0 - a :
This is the definition for the initial value of z for the Cubic
formula type.
Iteration
The iteration part of the formula is the middle, between the
initialization value and the final value. It is the processing
which takes the previous pixel location and computes the next
pixel location.
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Mandelbrot(XAXIS) { z = Pixel: z = sqr(z) + pixel, |z| <= 4 }
| | | | |
Name Symmetry Initial Iteration Bailout
Condition Criterion
For the Mandelbrot fractal, the iteration formula is--
z = sqr(z) + pixel
Here, z is either the initial value or is the result of the last
iteration. "Pixel" is the location (in complex space) of the
last
screen pixel position.
There are many, many variations of the iteration formula. Some
of
these are:
z = sqr(z) + (-0.74543, 0.2)
z = z*z + (0.11031, -0.67037)
z = sqr(z) + c
z = (pixel ^ z) + pixel,
z = c * sqr(z) + pixel,
z = z-p1*(s/(c-(s*s)/(c+c)))
z = z - p1 * ((z7-z)/
((7.0*z6-1)-(42.0*z5)*(z7-z)/
(14.0*z6-2)))
and many others are possible. For details about defining
iterations, see a textbook on Fractal Geometry.
Bailout Criterion
The bailout criterion is one of the methods by which it is
determined when to stop iterating the iteration formula. The
other principal method is to stop when the number of iterations
reaches some value. Also, if calculation of the iteration
produces a value equal to the initial value then iteration also
stops--this situation is called a periodic loop.
The most common definition of the bailout criterion is:
|z| <= 4
Thus iteration will continue until the absolute value of the real
part of z reaches or exceeds 4.
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Another common bailout definition is:
|z| <= P1
in which the newly computed value of z is compared with the
Parameter 1 value which the user entered (or defaulted).
Occasionally, other methods of doing the bailout comparison are
also used, for example:
.004 <= |t1 - t2|
where t1 and t2 are complex variables defined in the
initialization section.
Examples
The descriptions above have been of the three separate parts of
a fractal formula definition: the initialization, iteration, and
bailout condition. The following shows the complete definition
of
some typical fractals, starting with the Mandelbrot type:
Mandelbrot(XAXIS) = {
z = Pixel:
z = sqr(z) + pixel,
|z| <= 4
}
Note that this is just for the Mandelbrot--no corresponding Julia
is defined (as indicated by the lack of the c variable). Note
also that the separator between the iteration and the bailout is
a comma here but a semi-colon can also be used. The
initialization always terminates with a colon.
The definition of the MarksMandelPwr formula is:
MarksMandelPwr (XAXIS) {
z = pixel, c = z ^ (z - 1):
z = c * sqr(z) + pixel,
|z| <= 4
}
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Another full formula definition is:
NewtonSinExp (XAXIS) {
z = pixel:
t1 = exp(z);
t2 = sin(z)+t1-1;
z = z-p1*t2/(cos(z)+t1),
.0001 < |t2|
}
The following is a table showing the formulas for the fractal types
which are listed directly on the <t> list and not as part of the
formula.frm file. Note that the description of these formulas is
in mathematical notation, not that used for describing a formula
within a formula file.
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************************************************************************
Fractal Type(s) Formula(s) used
----------------------- -------------------------------------------
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))
Mandel, Julia z(n+1) = z(n)^2 + C
Mandelfn, Lambdafn z(n+1) = Lambda*fn(z(n))+C
where fn={sin,cos,sinh,cosh,exp,log,sqr}
MandelLambda, Lambda z(n+1) = (C) * (z(n)^2) + C
MarksMandel, MarksJulia z(n+1) = (C^(Period-1)) * (z(n)^2) + C
where "Period" is a parameter
Mandel4, Julia4 z(n+1) = z(n)^4 + C
Manfn+exp, Julfn+exp z(n+1) = fn(z(n)) + e^(z(n)) + C
Manfn+zsqrd, Julfn+zsqrd z(n+1) = fn(z(n)) + z(n)^2 + C
manowar c = z1(0) = z(0) = Xcoord + i*Ycoord;
z(n+1) = z(n)^2 + z1(n) + c;
z1(n+1) = z(n);
Manzpower, Julzpower z(n+1) = z(n)^M + C (M is a parameter)
Manzzpwr, Julzzpwr z(n+1) = z(n)^z(n) + z(n)^M + 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
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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))
Sierpinski z(n+1) = (2x, 2y - 1) if y > .5
else (2x - 1, 2y) if x > .5
else (2X, 2y)
spider c(0)=z(0)=pixel; z(n+1) = z(n)*z(n) + c(n);
c(n+1) = c(n)/2 + z(n+1)
tetrate z(0) = c = pixel; z(n+1) = c^z(n)
**********************************************************************
Special Cases
Cmplxmarksmand and Same as MarksMandel and MarksJulia except
Cmplxmarksjul period parameter is complex rather than real
Mandel4/Julia4 Special case of manzpower/julzpower (M=4)
popcornjul Julia calculation from the popcorn formula.
**********************************************************************
For a description of the formulas for the orbit fractals (such as
Henon, Rossler, Lorenz, see the description of the INITORBIT option.
For a description of certain other formulas, see Part III of this
Guide. This applies to the following fractal types:
UNITY, BIFURCATION, BIF, PLASMA, DIFFUSION, JULIBROT,
KAMTORUS, and MAGNET
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FULLCOLOR=y|1
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The FULLCOLOR option causes the image to be saved as a Targa
lightfile. By default, the name will be fract001.tga unless you
change it.
FULLCOLOR=y
This option lets you 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. A good map file to use is topo.map.
Valid with any light source FILLTYPE.
FULLCOLOR=1
This 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.
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, fullcolor files also have the background set to sky
blue.
Files which are created with the fullcolor option are very large, with
3 bytes per pixel. The file is created using Fractint's disk-video
caching, but is always created on the hard disk (expanded or extended
memory is not used).
When the FULLCOLOR option is 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.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
FUNCTION=sin|cos|sinh|cosh|exp|log|sqr
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option specifies which mathematical function is used to create a
fractal. The functions are:
sin sine
cos cosine
sinh hyperbolic sine
cosh hyperbolic cosine
exp exponential (e^x)
log natural logarithm
sqr square root
The syntax of this option allows for the entry of four function names,
one for each of the four parameters (see PARAMS). Thus, the syntax
is:
FUNCTION=f1/f2/f3/f4
in which f1 is used for Param1 and so forth. The default is:
FUNCTION=sin/sqr/sinh/cosh
These functions apply to the family of fractal types which usually
have "fn" in the type name. These are:
fn(z*z)
fn*fn
fn*z+z
fn+fn
julfn+exp
julfn+zsqrd
lambdafn
mandelfn
manfn+exp
manfn+zsqrd
manowar
spider
sqr(1/fn)
sqr(fn)
tetrate
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For example, the fractal type fn(z*z) means that the following
fractals can be created:
sin(z*z)
cos(z*z)
sinh(z*z)
cosh(z*z)
exp(z*z)
log(z*z)
sqr(z*z)
The term "z" is explained in the description of the FORMULAFILE
option.
Some of the fn fractal types take more than one function name, for
example fn*fn. For this type, there are 28 different fractals which
may created:
sin cos sinh cosh exp log sqr
sin 1 2 3 4 5 6 7
cos 8 9 10 11 12 13
sinh 14 15 16 17 18
cosh 19 20 21 22
exp 23 24 25
log 26 27
sqr 28
Obviously, fn1*fn2 and fn2*fn1 produce the same result so the bottom
of the table is empty.
When you select an fn fractal type from the list provided by the <t>
key then a parameter box will appear. It will request--
First function:
Bailout Value:
if only one function is used to define the fractal. If two are used
then the parameter box says:
First function:
Second function:
Bailout Value:
In addition, some parameter boxes allow you to enter values for the
real and complex numbers to be used.
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Usually, you set the FUNCTION option from within Fractint at the time
of creating a fractal. The FUNCTION option value is also written out
to frabatch when the <b> key is pressed for a fractal of this type.
About the only reason to use this option at the DOS prompt is when
converting a fractal from one function type to another--this can be
the only way to do it if bailout has been changed from the default and
you have zoomed in.
The lambdafn type calculates the Julia set of the formula
lambda*fn(Z), where lambda and Z are both complex. Two values, the
real and imaginary parts of lambda, should be given in the parameter
box. 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.
The mandelfn type is one of those for which pressing <spacebar> will
produce the Julia transform of the point at the center of the image or
zoom box.
The DECOMP option usually works quite well with these fractal types
and often produces both spectacular and unusual results.
Some of the functions are not all that reliable: log, in particular,
will often crash your system. The sin and exp functions can also at
higher resolutions. It's worth trying these functions anyway, but you
may wish to save any ram disks (or turn off some kinds of cache
programs) before the attempt.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
GIF87a=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Since Version 14.0, Fractint creates image files using the GIF89a
standard.
Files created using the earlier GIF87a standard can be read in with no
problem.
However, some GIF viewers cannot read GIF89a files. You can use the
GIF87a=y option to force Fractint to create the image file using the
older standard so that such a GIF viewer can read it.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
HALFTONE=freq/angle/style
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is useful only if you are printing images on a PostScript
printer. They tell the printer how to define its halftone screen.
The printer will default to appropriate values for these settings.
This option is useful only to one who is a diehard, inveterate tweaker
who can never leave well-enough alone.
The meanings of the three arguments are:
freq number of halftone lines per inch
angle screen lie angle
style halftone spot style
A value between 60 and 80 for the frequency produces good results.
A value of either zero or 45 degrees produce good results.
The style codes are:
0 - common circle screen (probably same as hardware default)
2 - horizontal line screen
4 - vertical line screen
Other values may be used--some work, some don't. They should produce
screens such as: boxes, crosses, or rounded crosses. Explore if you
like but don't expect wonders.
The default values are:
frequency = 80
angle = 45
style = 0
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
HAZE=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option has meaning only for Targa lightfiles.
The argument, nnn, must be between 0 and 100.
It is used to produce more realistic terrains by setting the amount of
haze for distant objects when using FULLCOLOR color in light source
FILLTYPES. It works only in the "y" direction currently, so don't use
it with much y rotation. Try ROTATION=85/0/0.
If you selected the FULLCOLOR option, you have a few more choices. The
next is the haze factor. Set this to make distant objects more hazy.
Close objects won't be affected very much, but distant objects will.
0 disables the function. 100 is the maximum effect, the farthest
objects will be lost in the mist. Currently, this does not really use
the distance from the viewer, but uses the y value of the original
image. So the effect really only works if the y-rotation (set earlier)
is between +/- 30.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
HERTZ=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is a sound choice.
It adjusts the tone produced by the SOUND option. Legal values are
200 through 10000. Use 440 if you plan to tune an orchestra at the
same time.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
IFS=filename
IFS3D=filename
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
IFS (Iterated Function System) fractals are among the most interesting
and popular.
They are also called Barnsley fractals in honor of Michael Barnsley
and his co-workers at the Georgia Institute of Technology.
IFS fractals are made of individual dots and form patterns like a
fern, spiral, leaf, and other natural shapes. The pattern is created
by taking a simple geometric shape and iterating it. This maps a
region of two-dimensional space onto itself. It is an affine
transformation of a space.
IFS fractals are described by a set of numbers which are read in by
Fractint from an external file. These files have .IFS as the filename
suffix. The following IFS files come with Fractint:
binary.ifs
coral.ifs
crystal.ifs
dragon.ifs
fern.ifs
floor.ifs
koch3.ifs
spiral.ifs
swirl5.ifs
tree.ifs
triangle.ifs
zigzag2.ifs
The default IFS file is fern.ifs. You can load a different IFS file
from the command line--
fractint ifs=binary.ifs
This will only change the default IFS file for that execution of
Fractint. Thus, when Fractint comes up it will present the default
Mandelbrot fractal.
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If you then press <t> to obtain the list of fractal types and then <i>
to move the highlight to the IFS type. You can also move the
highlight to this choice with the <arrow> keys. Pressing <i> works
only because IFS is the first (in fact, only) fractal type which
begins with the letter "i".
From the command line, you can both specify the name of the IFS file
but also cause Fractint to come up with an IFS fractal displayed, for
example:
fractint type=ifs ifs=binary.ifs
Anyway, back to the <i> key--since this key has two uses which must be
distinguished. The <i> key above was a speedkey used to move the
highlight to the IFS fractal type on the list. Pressing <Enter>
causes an IFS fractal image to be displayed. By default this is the
fern.ifs. If you have entered ifs=binary.ifs on the command line then
it will be the binary IFS.
While the image is developing you can press the <i> key. This time it
brings up the "IFS and 3D Parameters" box. The three menu choices
within this box are:
2D IFS Codes
3D IFS Codes
3D Transform parameters
By default, the highlight is on the third choice. If you move it to
the first item and press <Enter> you will get the "2D IFS Parameters"
box. This is also called the IFS Editor.
The IFS Editor lets you select an IFS file for display. If you press
the <r> key you will get a listing of all IFS files in the current
directory. Actually, IFS files will be found if they are kept
anywhere along the DOS path. You can also keep IFS files in a
separate subdirectory and its name will appear on the list (provided
the current directory is its direct parent). If you do, then simply
move the highlight to the subdirectory name and press <Enter> to view
a list of the IFS files there.
To select an IFS file, move the highlight to its name and press
<Enter>. It will immediately begin displaying. If you press <i>
again then the "IFS and 3D Parameters" box will appear and this time
the highlight will be pointed at the last menu choice, so simply press
<Enter> to obtain the IFS Editor.
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The IFS Editor shows you the codes for the current fractal. There are
four lines and seven columns of numbers. For example, for the
fern.ifs fractal, the values are:
# a b c d e f prob
1 0.00 0.00 0.00 0.16 0.00 0.00 0.01
2 0.85 0.04 -0.04 0.85 0.00 1.60 0.85
3 0.20 -0.26 0.23 0.22 0.00 1.60 0.07
4 -0.15 0.28 0.26 0.24 0.00 0.44 0.07
The number in the # column is the line number. The fractal
coefficients are in columns a through f. The probability value is in
the last column. The a,b,c,d,e,f,p parameters are standard ones for
defining Barnsley fractals. So much so, that several other fractal
generating programs besides Fractint can be used to generate IFS files
which Fractint can read and display. The Fractal Grafix, Fractal
Design, and Fractal Image (FGRAFIX, FRACTIMG, and FRACDSGN) programs
all can create interesting IFS files.
The text below this table says:
Enter the number of the line you want to edit
or R to start from another (.IFS) file, or S to
save your edits in a file, or ENTER to end==> _
If you enter a line number and press <Enter>, for example:
Enter the number of the line you want to edit
or R to start from another (.IFS) file, or S to
save your edits in a file, or ENTER to end==> 1<Enter>
then a prompt will appear below this block of text which says:
Parameter a: _0.00
Here the underscore shows the cursor location. You can enter a new
value or accept the current value by pressing the <Enter> key. When
you do this prompt will change to:
Parameter b _0.00
Since the value in column b of Line 1 of the table for the fern IFS is
a zero.
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If you wish to change a particular column value (such as column f)
then when this prompt first comes up you can step across the line by
pressing <Enter> repetitively until the prompt displays the current
value for column f.
The last prompt is:
Probability: 0.01
where the value shown is the current probability value. You can enter
a new value if you wish. After you press <Enter> then the parameters
will begin being evaluated--the image you have requested will begin to
display.
You can go through a pretty quick cycle:
.... fractal is drawing ....
<i> obtain "IFS and 3D Parameters" menu
<Enter> select highlighted choice
<1><Enter> to edit line 1
Parameter a accept or change a parameter
<Enter> repeat for parameters b-f
Probability: accept or change probability value
<Enter>
.... fractal is drawing ....
Thus, you can set and reset the parameters to your hearts content,
quickly seeing the results of each change since IFS fractals are
pretty quick to develop. When you find an image you wish to save,
press the <s> key as usual to save the image to a file.
The fern IFS has four parameter lines. An IFS definition can have up
to 32 lines of parameters--although usually 3-4 lines is enough. No
matter how many lines there are, the total of all of the probability
values should add up to 1.00. Thus, for the fern IFS, the
probabilities of the four lines are .01 + .85 + .07 + .07 = 1.00.
After you have entered parameter values which create a fractal which
is worth keeping, you can press the <s> key and the current parameters
will be written out to a file. When you press <s> a parameter box
comes up which says:
Enter the name of the .IFS file to save:
\fraint\fern.ifs
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The filename shown is the name of the last IFS file loaded. If you
press any qwerty key this name will be erased and you can enter a new
filename. You do not need the ".IFS" suffix--it will be appended for
you. If you do not use a full pathname then the file will be created
in the current directory.
You can also edit the file externally with any ASCII editor--just be
sure to preserve column alignment.
IFS fractals are zoomable, which is sometimes required because the
initial form can be rather small. You can ROTATE, SHIFT, or change
the PERSPECTIVE of an IFS fractal. 3D IFS fractals are also
particularly good with red/blue funny glasses. You can set 3D
parameters with the "Transform parameters" menu choice on the "IFS and
3D Parameters" menu.
You cannot use a disk video mode to write the image directly out to a
file.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
IFSCODES=N/a/b/c/d/e/f/g/h
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option allows you to enter IFS codes at the command line. The
first argument is the number of codes to follow and then N number of
ifs codes are entered, followed by slashes.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
INITORBIT=nnn/nnn
INITORBIT=pixel
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option lets you alter the initial point from which an orbit is
calculated for fractals in the Mandelbrot family.
It lets you change the shape of the Mandelbrot fractal. For example,
if you enter--
fractint initorbit=0.01/0
then the head of the snowman will be distorted into a teardrop shape
and the north and south radicals will be reduced. At other values all
of the radicals can be reduced so that they barely exist, for example
if you try:
fractint initorbit=0.001/.001
then the lake will appear without any radicals. If you try setting
initorbit=-1.7/0 then the Mandelbrot will be very small and offset to
the left. You will have to zoom just to see it. Has nice details,
though.
The first example above, with initorbit=0.01/0 is perhaps the best of
any for viewing orbits. Begin the image with this command and as soon
as the image starts developing, press the <o> key. This key is a
toggle and will turn orbit display off if you press it again. The
orbits as shown as they are being calculated. You should also change
the PASSES option from the default "g" to either a "1" or "2" before
pressing the <o> key, otherwise Fractint's internal calculations will
automatically skip over the most interesting orbit displays.
In this example, they are clearly spirals, whorls, and similar
shapes. For other settings of initorbit these orbit patterns are not
so clear.
The default setting for this option is--
fractint initorbit=pixel
This will produce the common Mandelbrot. If you use this argument you
must use all five letters in "pixel" and not just the first.
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If you press the <o> key while it is developing, the orbits are
visible but the patterns are not quite as distinctive as with
initorbit=0.001/0.
A fractal is created by iterating some formula:
z = f(z)
However, before iteration can begin some initial value must be
assigned by z. This initial value is called z(0). Within a
FORMULAFILE the value of z(0) is explicitly set in the definition of
the formula to be evaluated.
The initial value, z(0) is a complex number--it is a location in the
complex space of a fractal. Most commonly, the initial value is set
to be that of the coordinates of the point at the upperleft corner of
the fractal, thus:
initorbit=pixel
where "pixel" is a keyword which means "the location at the upperleft
corner of the fractal image". You can also specify that the initial
value be at the center coordinates of the fractal, thus:
initorbit=0.00/0.00
The value to which you are setting initorbit is a location. If you
set initorbit=pixel then the first orbit will begin at the location
(in complex space) of the upperleft corner of the image. If you enter
initorbit=.5/0 then the first orbit will begin at location (.5,0)
where this is a complex number specifying a location in the complex
space in which the Mandelbrot exists.
Try the fractal:
fractint type=lambdafn function=sin initorbit=.5/.5 inside=0
You will obtain an image with a large lake. Now add:
inside=attractors
with the <x> menu or by adding this option to the command line. 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. Next, press <o> to see that initial points of
all of the orbits converge at the point of the finite attractor.
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If f(z) is a generalization of the formula which is iterated to create
a fractal then fk(z) is the result of k iterations of the formula.
Here the "k" should be read as if it were a subscript. If the
function involves both z and c then the general function is fkc(z),
again where k is a subscript.
Now define g(z) in which the function "g" is defined as:
g(c) = inf { |fkc(0)|: k=1,2,3,...}
Thus, it evaluates as the absolute value of evaluation of the function
fkc(z) where z=0 for all values of the index k from 1 to infinity.
This results in the greatest lower bound. The result, g(c), is the
closest to the origin which any point in an orbit which starts a zero
gets. The value of k for the iteration at which g(c) reaches its
closest point is called the index(c). The "inf" in the formula
definition stands for the "infimum" operation.
Some of the pixel coloring schemes for the inside color (such as
INSIDE=bof60) use index(c) to determine the color to be used to color
the corresponding screen pixel. It produces bands of color where the
value of index(c) is the same throught each band.
Similarly, INSIDE=bof61 shows domains in which index(c) is a constant
value. These are areas in which the iteration when the orbit goes
closest to the origin has the same value.
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 option. 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
he first two parameters.
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The orbit option has different implications for different kinds of
fractals. These are mentioned below for several fractal types.
NEWTBASIN
When you press <t> and select this fractal type from the list you will
get a parameter box. The first value is the order of the equation--
thus if you enter a 5 then the fractal will have 5-way symmetry. This
order must be an integer from 3 to 10. In general, odd values give
aesthetically more pleasing results. The second parameter is a flag
which turns on or off a feature which shows alternating colors which
correspond to the number of iterations needed to attract an orbit.
All pixels within the same band have the same number and so are
colored alike. The values here are 0 to turn it off (the default) and
1 to turn it on.
MANDELLAMBDA
This type is the "Mandelbrot equivalent" of the lambda set.
Almost all the Fractint "Mandelbrot" sets are created from orbits
generated using formulas like:
z(n+1) = f(z(n),C)
in which z(0) and c are initialized to the complex value corresponding
to the current pixel. This assumes that Mandelbrots are maps of the
corresponding Julia and each pixel of the "Mandelbrot" is colored the
same as the Julia set corresponding to that pixel. Note that this
definition differs somewhat from a common one in which z(0) is
initialized to a critical point at which the derivative of the formula
is zero. For the formula above, this critical point is at location
(.5, 0). The Mandelambda type is calculated with this initialization
of z(0). For all of the other Mandelbrot-type fractals, the
initialization is:
z(0)=pixel
Actually, for the default Mandelbrot, both methods of initializing the
first value of z produce the same result.
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POPCORN
These fractals are plots of 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 of the complex values
within the "corners" values, and h=.01. All of these orbits are
superimposed--this results in the "popcorn" effect.
You may want to use a maxiter value less than normal (Pickover
recommends a value of 50) when computing a Popcorn fractal.
The popcorn is best viewed by pressing <o> to turn on the View Orbits
option.
Although you can zoom on a Popcorn image or rotate the image, the
results may not be what you'd expect because of the superimposing of
orbits and arbitrary use of color.
POPCORNJUL
This type is the Julia set generated by the same equations used for
Popcorn. The usual escape-time coloring is used.
This fractal has excellent details and you can make hundreds of
swell-looking images here.
KAMTORUS
KAMTORUS3D
These are implementations of the Kam Torus in both two- and three-
dimensional variants.
The fractal is created by superimposing orbits generated by a set of
equations, with a variable incremented each time, thus:
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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, the value of "orbit" is incremented by a step size.
The parameters may be set by the user when creating a Kamtorus image.
The parameter box contains:
Angle (radians) 1.3
Step size 0.05
Stop value 1.5
Points per orbit 150
The default values are shown on the right. In general, setting the
number of points high and then zooming in on an interesting area
produces the best results.
You can also create fractal music by using SOUND=x and varying the
stop value. For instance, try a stop value of 5.
The 3D variant is created by treating 'orbit' as the z coordinate.
LORENZ
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 eventually reduces the best weather forecast to
rubble. A storm developing over North Dakota is affected by the wind
blowing past a skyscraper in Melbourne, Australia. As a result, it
will later pass over Alabama instead of Maryland.
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 this variable as time then the solution traces an
orbit which is made up of two spirals at an angle to each other in
three dimensions. The orbit color is changed as time goes on to add a
little razzmatazz to the image.
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The equations are:
dx/dt = -a*x + a*y
dy/dt = b*x - y -z*x
dz/dt = -c*z + x*y
These differential equations are solved approximately using a method
known as the First Order Taylor Series.
Here, the notation for the derivative dx/dt is treated as if it really
were a fraction, with "dx" the small change in x that happens when the
time changes "dt". Multiplying the above equations by dt and you will
have the change in the orbit for a small time step.
The time step is added to the old vector to get a new vector after
each 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)
The successive points are connected with a line. The result is
projected in 3D for a 3D image. The attractor orbit may be seen in 3D
by using red/blue funny glasses.
In 3D, you can ROTATE the image, change its PERSPECTIVE, or SHIFT it.
The default PERSPECTIVE=60/30/0 settings are not the best for viewing
Lorenz3d fractals. Instead, start with ROTATION=0/0/0 and then change
to ROTATION=20/0/0 (or =40/0/0) to see the attractor from different
angles. Next, try a PERSPECTIVE=100 to get inside of the image.
Actually, any perspective value greater than 1 can be used. You may
also wish to turn SOUND=x on and (if you're really into tweaks) change
the tone with HERTZ=300.
When you select a Lorenz (or Lorenz3d) fractal type from the list
provided by the <t> key you will get a parameter box which contains:
Different Lorenz attractors can be created using different parameters.
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Four parameters are used. Within the Parameter Box which comes up
when you select the lorenz type from the list provided by the <t> key,
are the following parameters:
Time Step 0.02
a 5
b 15
c 1
Here "Time Step" refers to the dt argument in the formula equation
given above. In fact, a, b, and c are also found. That equation is:
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)
If you enter a Time Step (dt) value smaller than the default 0.02 then
plotting will be slower but more accurate; larger values are faster
and rougher.
The a, b, and c parameters are coefficients. If you change them, you
should make small, incremental changes to the default values (5,15,1)
rather than large changes. For example, try a=5,b=16,c=2 with a dt
Time Step of 0.001.
ROSSLER and 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.
This is the opposite of most of us.
A Rossler fractal looks like a band of ribbon with a fold in it.
The definition of the Rossler fractal type is similar to that of the
Lorenz type in that it is defined using the same four parameters. The
default values are:
Time Step 0.02
a 5
b 15
c 1
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Rosslers are computed by multiplying the equations by "dt" to solve
the differential equation and generate the orbit. This time we will
skip straight to the orbit generator. 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
Michel Henon was an astronomer at Nice observatory in southern France
who 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. Just like you.
The orbit traces out a characteristic banana shape, but on close
inspection, the shape is made up of thicker and thinner parts. Upon
magnification, the thicker bands resolve to still other thick and thin
components.
The equations that generate this strange pattern perform the
mathematical equivalent of repeated stretching and folding, over and
over again.
The equation is:
xnew = 1 + y - a*x*x
ynew = b*x
The default parameters are a=1.4 and b=.3.
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PICKOVER
Named after Clifford A. Pickover of the IBM Thomas J. Watson Research
Center is a a fractal created with a 3-dimensional orbit:
xnew = sin(a*y) - z*cos(b*x)
ynew = z*sin(c*x) - cos(d*y)
znew = sin(x)
The default parameters are: a = 2.24, b = .43, c = -.65, d = -2.43.
GINGERBREADMAN
This simple fractal came from Page 149 of the "Science of Fractal
Images" by Peitgen and Saupe.
The gingerbreadman contains infinitely many copies of himself at all
different scales.
xnew = 1 - y + |x|
ynew = x
There are no parameters.
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 fractal reaches the
edge of the screen.
During development of the image, you can press <o> to see the random
motion of the orbit. However, watching random motion is about as much
fun as peeling grapes.
The only parameter to diffusion is the size of the border between the
fractal and the edge of the box. If you make this number small,
thefractal will look more solid and will be generated more quickly.
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ORBITAL FRACTALS SUMMARY
The following table summarizes the equations for defining the various
kinds of orbital fractals:
Gingerbreadman Orbit generated by:
xnew = 1 - y + |x|
ynew = x
Henon Orbit generated by:
xnew = 1 + y - a*x*x
ynew = b*x
The default parameters are a=1.4 and b=.3.
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)
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
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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
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
INSIDE=0|-1|nnn|bof60|bof61
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option controls the color used for the "inside" of the Mandelbrot
and Julia fractals. This is the color of the lake and of the
filaments which connect all of the midget lakes. In addition, it
controls the appearance of lakes within Julia fractals.
You can find a Julia with a lake by moving the zoom box to the
shoreline of the Mandelbrot and locating it so that the center of the
box is over part of the lake and then pressing <spacebar>.
You can set this option internally by pressing the <x> key and
entering the argument on the line which requests "Inside Color".
The default color is blue. You may wish to change the default so the
inside is black since this is better for most purposes. The way to do
this is to use INSIDE=0 on the command line whenever you execute
Fractint. This same result can be accomplished by placing this option
in a @set file or in the SSTOOLS.INI file.
INSIDE=0
When you use the default color then when you turn color-cycling on the
inside color will cycle along with the rest. When the area of the
fractal colored the inside color is large (such as the lake of the
default Mandelbrot) the result is annoying unless you turn the color-
cycling speed way down. An advantage of using black is that it does
not color-cycle and simply stays black all the time. This is
aesthetically much more satisfying, especially at normal or high
cycling speeds.
Incidentally, the filaments which connect the lakes are usually thin
and sometimes not visible without magnification. You can artificially
enlarge the filaments with the DISTEST option. This is useful if you
are planning to make a printed black-and-white image of a Mandelbrot
fractal.
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INSIDE=-1
This sets the inside color to be that of maxiter. This is the
number of the maximum iteration. You can define this value
with the MAXITER option.
INSIDE=nnn
When using the default color map then the specific colors you
can set the inside to are:
0 black
1 blue
2 green
3 cyan
4 red
5 magenta
6 brown
7 light gray
8 dark gray
9 light blue
10 light green
11 cyan
12 orange
13 pink
14 yellow
15 white
to: 255 some color
INSIDE=bof60
Inside=bof60 colors the lake in alternating shades according
to the level sets of g(c). The term g(c) is defined in the
article about the INITORBIT option.
Both inside=bof60 and inside=bof61 are intended for use in
bringing detail out of the lake of a Julia.
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INSIDE=bof61
Inside=bof61 shows domains where index(c) is a constant. The
term index(c) is also described in the INITORBIT description.
BOF61, sometimes referred to as a "feathered inside" shows
where index(c) is constant, which organizes the sequence of
indices according to Fibonacci sequences.
INSIDE=attractor
Although it says in fractint.doc that you can set the inside
color to the keyword "attractor" in reality you cannot.
Instead, see the description of the FINATTRACT option.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
INTEROCULAR=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This is one of the red/blue funny glasses options. It can be adjusted
to compensate for the fact that human eyes are not a standard distance
apart.
You can adjust this value from within Fractint on the Funny Glasses
Parameters box. The prompt there is:
Interocular distance (as % of screen) 3
One reasonable constellation of options to try is:
BRIGHT = 100% / 100%
CONVERGE = -5
INTEROCULAR = 5
This option interacts with the CONVERGE option, so it will take some
fiddling to get it right.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
INVERT=radius/xcenter/ycenter
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option turns on inversion. It may also be set on the <y>
Extended Options and Doodads screen. The information is also
displayed with the <tab> key.
The arguments are:
radius the radius of inversion
xcenter x-coordinate of center of inversion
ycenter y-coordinate of center of inversion
Each of these may be a number or the keyword "auto".
On the <y> screen are the prompts--
Inversion radius or "auto" (0 means off) 0
Center X coordinate or "auto" 0
Center Y coordinate or "auto" 0
(use fixed radius & center when zooming)
To quickly see the effect of inversion, bring up the default
Mandelbrot and use <y> to enter "auto" for these three parameters.
After viewing the result you can then press <x> and set decomp=128,
and the combination produces interesting results.
The INVERT option performs a related transformation on most of the
fractal types.
You define the center point and radius of a circle and then Fractint
maps each point inside the circle to a corresponding point outside,
and vice-versa. This everts the plane.
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 fractal is turned inside out.
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You may set the radius to--
0 off (default value)
-1 default radius
auto radius autodetection
nn.nn specific radius value
On the <y> display, the default radius is 0 and therefore inversion is
turned off. If you enter a value of -1 then the radius will be set to
1/6 of the smaller screen dimension.
You may set the x and y coordinates to--
0 current screen center (default)
nn.nn specific x or y coordinate
Another example of inversion to try is:
fractint type=newton invert=1/0/0 params=27/0/0/0
this causes the center to explode out to the periphery.
By entering specific x- or y-coordinates you are relocating the center
of inversion, which often produces interesting effects. Note that
when you move the inversion center then you lose the ability to zoom.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ITERINCR=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The number nnn must be between 0 and 32000. It sets the iteration
increment.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
LATITUDE=nn/nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used when creating spherical fractals.
In standard orientation, the right edge of the globe faces North.
This is different that the Earth, on which the top edge of the globe
faces North. But then, fractals are their own little world.
The horizontal x-axis is the latitude. The vertical y-axis is the
longitude.
The nn/nn arguments are the minimum and maximum latitude.
The default latitude is -90/90. The default longitude is 0/180. This
is the full, normal globe. 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.
Suppose you use--
LATITUDE = -90/0
when you create a spherical image. The final image will cover only
the top half of the globe. The bottom half will be empty. However,
if you are careful, you can overlay another image on top of this one
where that image contains a bottom half of the globe. Heaven only
knows why you'd want to create a globe with two distinct halves.
If you use--
LATITUDE = 45/45
then the created image will appear between the Tropic of Cancer and
the Tropic of Capricorn. It will be a wide band around the equator.
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Actually, if you use--
LATITUDE = 10/10
then the image will be a narrow band. If you use --
LATITUDE=10/10 LONGITUDE=45/135
then the band will no longer cover the entire width of the equator--
it will be a rectangular block in the middle of the sphere.
To create an "icecap" at the top of the sphere (top meaning viewed as
if it were the Earth) use the following coordinates. With the fractal
sphere's north being to the east this means that its east is the
Earth's north. At any rate--
LATITUDE=10/10 LONGITUDE=165/180
will do this.
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
LFILE=lsystemfile
LNAME=lsystemname
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
If you press <t> while executing Fractint then a list of fractal types
will be displayed. One of the entries is:
l-system
If you pick this choice then a list of the l-system definition files
will appear. There is only one such file, named "fractint.l". If you
select its name then a list of the l-system fractals which are defined
within the file will be displayed.
The term "l-system" is short for "Lindenmayer systems" which were
named after the biologist Aristid Lindenmayer. L-systems are not
fractals but are closely related--they would be fractal if the order
were infinite. This method has five components:
1. An alphabet
2. An axiom
3. Transformation Rules
4. An order
5. A turtle
An alphabet is a set of string characters or variables.
An axiom is a seed string of initial alphabet characters.
Each character of the axiom is replaced by a string taken from the
table of transformation rules.
This is repeated iteratively the number of times specified by the
order number. The order is the number of times to cycle the rule.
Finally, a turtle draws the final character string on the screen.
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Typical l-system types are:
Koch3
Peano1
CantorDust
Snowflake1
Sierpinski1
When you pick one of these names then you will get a Parameter Box in
which you can enter the order to be drawn. Then the l-system fractal
will be displayed. If the fractal takes a while to develop then a
message telling you this appears and a little whirligig goes round.
The l-system fractals are all defined in a file named fractint.l. A
typical definition is:
Demo1 {
Angle 6
Axiom F--G--F
F=F+F--F+F
}
This looks more obscure than it actually is. The first line is:
Angle n
This sets the angle to 360/n degrees; n must be an integer greater
than two and less than fifty. Thus, the meaning of:
Angle=6
is the same as if it were written:
angle=360/6
which is 60 degrees. Note that either a blank or an = sign may
separate the term "angle" from the value. Also, "angle" can be
written in either lowercase or uppercase letters.
With this method of specifying the angle which the turtle can turn,
the angle is always a constant or a multiple of that constant. This
angle is represented by a + or - sign. Thus, for the example above:
+ means to turn 60 degrees to the left
- means to turn 60 degrees to the right
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If the sign occurs more than once then the angle increases in unit
chunks, thus:
++ means to turn 120 degrees to the left
+++ means to turn 180 degrees to the left
and so forth. These degree values are only accurate when angle=360/6
has been defined. If the angle unit were defined as angle=360/4 then
each + sign would indicate a 90 degree turn to the left.
The '+' increases the angle in a positive direction. Mathematically,
positive is counterclockwise which is also to the left.
The third line in the example above was--
F=F-F++F-F
This is the transformation rule and in this case it means--
F a line forward
- a right turn (60 degrees)
F a line
++ two left turns (120 degrees)
F a line
- a right turn (60 degrees)
F and a line
This rule is written: F-F++F-F
The result, the path of the turtle is--
_______ ______
\ /
\ /
\/
This is the result of the first cycle, the first iteration of the
rule. In the first iteration the meaning of "F" was a simple straight
line and therefore this turtle-path is composed of four straight lines
(one for each occurrence of F in the rule and three angle changes.
For the second iteration, the meaning of "F" is no longer a straight
line but is instead the entire curve produced as a result of the first
iteration. Thus, each F in the rule is replaced by "F-F++F-F"
therefore the turtle path for the second iteration is:
F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F
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If you break this string up into its constituent parts, they are--
F - F ++ F F
F-F++F-F - F-F++F-F ++ F-F++F-F - F-F++F-F
Here, the first line shows iteration 1. The second line shows
iteration 2 in which each original F was replaced by the
transformation rule. It follows from this that in the third iteration
each "F" of the second iteration is replaced by the entire second
iteration rule. This quickly gets too long and confusing-looking to
show here. Each "F" in the rule is replace by
F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F.
The rules do not change for each iteration. The rules stay the same.
Once you've gotten to F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F the next
generation replaces each F with F-F++F-F as before, not with the
longer string. Subsequent generations continue to use the same rules
on
the ever-growing base string.
Graphically, the result of the second iteration is (very roughly,
because of the limitation of ASCII characters):
___ __ __ __
\/ \ / \/
/_ _\
\/
and this begins to look like the Koch shape, which it is. In the
third iteration, each line segment is replaced by the entire result of
the previous iteration.
Naturally, this being Fractint and not the real world, there are some
bells and whistles added to this basic structure. One of these is
that you can specify arbitrary angles rather than a fixed angular unit
for when the turtle changes direction.
The easiest way to understand what an l-system definition is doing is
to obtain the plot with order=1 and then trace the turtle's path.
When you request an l-system drawing within Fractint, a parameter box
comes up in which you can enter the order. In generaly, you should
normally view the order=1 and order=2 versions of the l-system before
going on to the higher orders to get a feel for what is happening.
Also, higher orders tend to take progressively longer to develop. The
length of the string usually grows exponentially, so it is easy to
exceed the resolution of your computer.
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The "string" of turtle movement instructions is a sequence of
characters. The entire line must be no longer than 160 characters
long.
In the string, the letters "F" and "G" are drawing commands:
F means to draw forward
G means to move forwared without drawing
The meaning of the plus (+) and minus (-) signs are:
+ means increase the angle (i.e. turn left)
- means decrease angle (i.e. turn right)
Therefore the meaning of F--G++F is:
draw forward
decrease the angle twice
move forward
increase the angle twice
draw forward
Another example is:
angle=4
F+F+F+F+
This example performs the following steps:
draw a line (0 degrees)
increment angle by 360/4 (90 degrees)
draw a line
increment angle by 360/4 (180 degrees
draw a line
increment angle by 360/4 (270 degrees)
draw a line
increment angle by 360/4 (360 degrees; 0 degrees)
Thus, this example draws a square.
Other symbols which may be used in defining the string are:
D means to draw forward
M means to move forward without drawing
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Note that the system maintains two distinct angle counters. Thus,
both D and F may be used in the same rule but refer to different
angles. Similarly, both G and M may both be present and refer to
different angles of movement without drawing. The difference is
summarized in the following chart:
D draw forward by nnn angle
F draw forward by 360/nn angle
M move forward by nnn angle
G move forward by 360/nn angle
Thus, for D and M the angle is defined as a specific angle, such as 90
degrees. For F and G the angle is defined as a that of a pie-slice,
for example 360/4 (which also happens to be 90 degrees).
The meaning of the backslash (\) and forward slash (/) signs are:
\nnn means to increase the angle by nnn degrees (i.e. left)
/nnn means to decrease the angle by nnn degrees (i.e. right)
For example:
D\90D\90D\90D\90
describes the following steps:
draw a line (0 degrees)
increase angle by 90 degrees (90 degrees)
draw a line at this angle
increase angle by 90 degrees (180 degrees)
draw a line at this angle
increase angle by 90 degrees (270 degrees)
draw a line at this angle
increase angle by 90 degrees (360 degrees; 0 degrees)
in other words, this example also draws a square. If this example had
been written as:
D\90D\90\90D\90
then the third (left) side of the square would not be drawn--the
result would be a three-sided square with the left side absent.
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Another example is:
angle 6
axiom F
F=FGF
This means that "F" is to be transformed by the rule "FGF", which is
clearly iterative. This rule is the basis for the CantorDust l-
system fractal. As a first order fractal, it is simply two drawn
lines separated by a move, thus the result is:
_____________________ _______________________
When this same rule is evaluated as a second order, then the result
is:
_______ ______ _______ _______
When this same rule is evaluated as a third order, then the result is:
__ __ __ __ __ __ __ __
and so forth.
Other symbols which may be used in defining the transformation rule
are:
| means to turn 180 degrees (if possible)
! means to reverse angular direction
The | symbol turns the largest angle possible which is less than or
equal to 180 degrees. Thus, if you define the pie-slice angle as
360/7 then using | is equivalent to using +++ since 360/7 = 51.43
degrees and three times 51.43 is 154.43 degrees. Since ++++ is 205.72
degrees and is greater than 180 degrees, the largest value under 180
is +++. The | symbol only affects angles defined using the pie-slice
method and not angles specified numerically. Thus, it affects the +
and - angles but not the \ and / angles since these are defined with
specific angles.
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The ! symbol causes the meanings of the + and - signs to reverse.
The ! also causes the meaning of / and \ to exchange. So, anytime you
have two !'s with no angle characters between them, nothing will
happen. When you look between pairs of '!' chars, (starting from the
beginning) you can see that there are angle commands between them.
By default, the length (i.e. size) of the line segment drawn is a
certain length. You can specify the length of the segment to be drawn
with the notation--
@nnn
in which nnn is a factor which indicates how much the standard segment
size is to be multiplied by. For example:
@2 -- twice standard size
@0.5 -- half standard size
@1.333 -- one and a third standard size
@.1 -- one tenth standard size
and so forth.
In addition to being a numeric value, nnn may also be the codes I or
Q. The character "I" indicates the inverse of the number, thus:
@I10 -- one tenth standard size (i.e. 1/10)
@I2 -- one half standard size (i.e. 1/2)
@I3 -- one half standard size (i.e. 1/3)
and the code "Q" represents the square root operation, thus:
@Q9 -- 3 times standard size (sqrt(9) = 3)
@Q25 -- 5 times standard size (sqrt(25) = 5)
@IQ2 -- 1/sqrt(2) times standard size
@IQ9 -- one third standard size (1 over sqrt(9) equals 3)
Finally, an advanced pair of symbols which may be used are square
brackets. The left square bracket means to push the enclosed angle
onto a stack and the right square bracket means to pop it off.
The [ preserves the current turtle state: position, draw size, +-
angle, and /\ angle. The ] restores the last set of preserved values.
Anything can be inside the [] pair -- not an "angle". This function
is used for tree like things, where you want to draw a branch, and
then come back to the main tree part.
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Another advanced option concerns color control. Thus--
Cnnn means use color nnn
therefore C0 always means to use black. The color numbers from 1 to
255 correspond to specific colors depending upon the color map
currently in use.
You can increment and decrement the color number automatically, thus:
<nnn means to increment the color number by nn
>nnn means to decrement the color number by nn
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 '}'.
You can define a null, empty string. For example--
F=
defines F as an empty string.
A line which starts with ;; is a comment line.
An example of a complete l-system definition is:
;; This is the Hilbert l-system.
Hilbert {
axiom x
x=-YF+XFX+FY-
y=+XF-YFY-FX+
angle 4
}
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oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
LIGHTNAME=filename
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The name of the Targa-24 file to be created when using FULLCOLOR with
LIGHTSOURCE.
Unless you use this option, the first Targa lightfile you create will
be named light001.tga. Similar to the name fract001.gif used for GIF
files, the name will automatically increment as you create other Targa
lightfiles.
If you use, for example, the option LIGHTNAME=MYLITE then the first
Targa lightfile created will be named MYLITE01.TGA.
The background color of a Targa lightfile will be sky blue.
You can also set the lightsource filename from within Fractint. To do
so, first press <3> to obtain the 3D Mode Selection screen. When you
next press <Enter> you will get the Select 3D Fill Type screen. If
you move down to the last two items on this list, they are:
light source before transformation
light source after transformation
If you select one of these and press <Enter> you will get a screen
with a box which requests that you enter a MAP file to be used. After
doing this you will obtain the Planar 3D Parameters screen. The last
choice on this list is--
Color/Mono Images with Light Source (1=Color)
if you enter a 1 after this field and press <Enter> then you will
obtain the Light Source Parameters screen. The last choice listed is:
Full Color Light File Name (if not light001.tga)
The default entry is light001.tga and you can overwrite this with
another name.
See also: FULLCOLOR, LIGHTSOURCE, 3D
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LIGHTSOURCE=xx/yy/zz
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used to define where the source of light is coming from
when creating a Targa lightfile image. It may be used with any 3D
fractal type.
The x, y, and z directions are scaled the same as the image. For
example, LIGHTSOURCE=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 you use 90/90/30 then 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. It will be in the early morning sun
position. (Or late afternoon sun position, it's kinda hard to tell.)
You can also set the light source from within Fractint. To do so,
first press <3> to obtain the 3D Mode Selection screen. When you next
press <Enter> you will get the Select 3D Fill Type screen. If you
move down to the last two items on this list, they are:
light source before transformation
light source after transformation
"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.
"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.
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If you select one of these two choices and press <Enter> you will get
a screen with a box which requests that you enter a MAP file to be
used. After doing this you will obtain the Planar 3D Parameters
screen. The last choice on this list is--
Color/Mono Images with Light Source (1=Color)
if you enter a 1 after this field and press <Enter> then you will
obtain the Light Source Parameters screen. The items listed here are:
X value light vector
Y value light vector
Z value light vector
and the defaults are 1/-1/1. These are the same three values as
defined with the LIGHTSOURCE=xx/yy/zz batch option.
See also: SMOOTHING, AMBIENT, FILLTYPE, FULLCOLOR, LIGHTNAME,
RANDOMIZE, 3D, HAZE, LIGHTNAME
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LOGMAP=y|old|n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The LOGMAP option compresses the color palette. The fractal image
appears unchanged except at the shoreline of the lake.
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".
The possible arguments are:
logmap=y
logmap=n
logmap=old
logmap=1
logmap=-1
logmap=n
logmap=-n
logmap=0
where n is greater than 2.
logmap = yes
logmap = no
logmap = 1
These three are synonyms.
They specify the new standard logarithmic palette. Which
"spreads" the low color numbers.
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logmap = -1
logmap = old
These two are synonyms.
They specify the old standard logarithmic palette. It differs
from logmap=1 in that the low numbered colors are not used.
logmap = n
This is the same as logmap=1 except that it doesn't go into
effect until iteration n. Pixels with iterations less than n
are set 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
This is similar to logmap=n, but uses a square root
distribution of the colors instead of a logarithmic one.
High values of -n or n let you hunt for midgets, but at the
price of seeing tendrils.
logmap = 0
This is the default and it turns logarithmic mapping off.
When using a compressed palette in a 256-color mode, you should change
the 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.
You can set the LOGMAP option from within Fractint on the <x> Options
and Doodads screen.
Super-high iteration limits (like MAXITER=30000) are useful when using
logarithmic palettes.
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LONGITUDE=nn/nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This is the same as LATITUDE except it goes up and down instead of
across.
See also: LATITUDE
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MAP=filename
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
A map is a set of 256 colors which are used to color the fractal. A
map file is an external file which contains the R,G,B color codes for
each of the 256 colors. Fractint comes with the following map files:
ALTERN.MAP
CHROMA.MAP
DEFAULT.MAP
FIRESTRM.MAP
GAMMA1.MAP
GAMMA2.MAP
GLASSES1.MAP
GLASSES2.MAP
GOODEGA.MAP
GREEN.MAP
GREY.MAP
GRID.MAP
LANDSCAP.MAP
TOPO.MAP
In addition, it is likely that you would create other map files of
your own.
The beginning contents of the DEFAULT.MAP file is:
0 0 0 The default VGA color map
0 0 168
0 168 0
0 168 168
168 0 0
168 0 168
168 84 0
168 168 168
84 84 84
These are the RGB color codes for the first 10 colors. The first
color is always black. The three numbers are the values of the three
components of each color: RED, GREEN, and BLUE. Each component is a
value from 0 to 255.
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The map file contains ASCII text and may be edited with any external
ASCII editor. You can also edit the file internally from within
Fractint by using the Palette Editor. This feature was described in
Part I of this manual.
You can change maps from within Fractint with the <l> "ell" key. It
brings up a list of the map files in the current directory. If you
keep your map files in a subdirectory then its name will be listed and
you can view its contents by selecting the subdirectory name.
You can change maps only during color-cycling. Thus, press <c> to
start cycling before pressing the <l> key. When the new map comes up
the initial color pattern is the one for which it was named. After
you press <Enter> while color-cycling then the colors will be
shuffled. Thus, if you load the GREEN.MAP then the predominant color
in that map is (surprise!) green. After you press <Enter> the result
will not usually be greenish any longer.
Several of the maps supplied with Fractint have special purposes.
Some maps are designed primarily for 3D red/blue glasses viewing.
These are the GLASSES1 and GLASSES2 maps. Generally glasses1.map is
for type 1 (alternating pixels), and glasses2.map is for type 2
(superimposed pixels) 3D fractals.
Other maps are intended for use in creating fractal landscapes or
planets. Such maps are TOPO and LANDSCAP.
The CHROMA map is all of the rainbow colors in order and contains no
sudden color changes. It has several uses. For one, you can use it
to create new maps using the palette editor. The CHROMA map is the
only one which works well with fractals which have large areas of the
same color.
The DEFAULT map is a nicely spectacular one. You can change the
default map either by naming some other map to the name DEFAULT.MAP or
by using MAP=other on the Fractint command line, where "other" is the
name of some other map file. You can load the default map quickly
from within Fractint by pressing the <d> key while color-cycling.
Note that if you are not color-cycling then pressing <d> will cause
you to exit temporarily back to DOS. To return, type "exit".
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The ALTERN map is black-and-white monochrome. It can be loaded by
pressing the <A> key while color cycling. Pressing <A> always loads
ALTERN.MAP, no matter what the contents of the file by that name is.
The GAMMA1 and GAMMA2 maps serve the same purpose as the ALTERN map.
When you create a starfield image (by pressing the <a> key), Fractint
automatically loads the ALTERN.MAP and will abort if the file cannot
be found. These maps are useful for viewing with red/blue funny
glasses. The ALTERN.MAP contains the "famous" Peterson-Vigneau
Pseudo-Grey Scale.
GRID.MAP is intended for stereo surface grid images. Use it for
wire-frame images using 16 color modes.
When a fractal image is saved with the <s> key, the current map is
also saved with it so that when it is restored it will appear in the
colors you saved it with and not the default colors.
When you use MAP=filename on the Fractint command line then the map
file named becomes the default map for that execution.
When you press the <b> key to write the current parameters to the
frabatch file, the map name is not written. If you want a MAP= option
to appear on the command line, you should edit frabatch.bat to put it
there.
Incidentally, if you have a Targa board you cannot color-cycle. This
is because the color-mapping schema for this board is different from
the rest. You can, however, use map files to load different color
patterns.
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MAXITER=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This is the maximum number of iterations allowed for evaluation of the
fractal-generating formula. The default is 150. The maximum value is
32000. The minimum value is 10.
For some fractals, changing the maxiter value can have a dramatic
effect on the appearance of the image, but for other fractals changing
this value doesn't do diddle. Basically, you must simply experiment
with the effects of changing it.
In general, higher values produce greater detail. In some cases, the
detail computed is greater than the detail which your monitor can
display, in which case the excess detail simply wastes development
time.
In general, higher values make the fractal take longer to develop, but
again, not always. For some fractals, it has no effect. For some
fractals the maxiter value is never used since the iterating always
stops for some other reason before reaching the max iteration value.
Reaching the maxiter value is usually one one of several possible ways
in which an iteration may "escape" and cease iterating.
If you use both a high maxiter and the distance estimator method
(DISTEST=) then development can be rather slow, even on a fast machine
with a math coprocessor. With Fractint for DOS there is also a memory
limitation since Fractint does not use more than 640K of memory. This
is not true of Fractint for Windows.
Especially for decomped fractals, you may wish to set maxiter to a
very low value (such as 10) and then try increments of 1.
Super-high iteration limits (like MAXITER=30000) are useful when using
logarithmic palettes.
See also: INSIDE=maxiter
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OUTSIDE=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option causes the Mandelbrot fractal to be displayed in only two
colors. Everything inside of the M-set is one color and everything
outside is the other. This is instructive and you should try it with
the default Mandelbrot at least once.
The nnn argument is the number of a color, thus:
OUTSIDE=15
INSIDE=0
will cause the outside to be white and the inside black.
You can set the outside color on the <x> parameter screen. It would
be rare to use this option on the command line.
Mathematically, no information is lost when all points outside of the
set are the same color. Of course, aesthetic information is lost.
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OVERWRITE=n|y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
By default, Fractint will not save an image into an existing file but
always creates a new file. If you set OVERWRITE=y then the name you
tell Fractint to use to save the file will be used even if a file of
that name already exists.
By default, the first image file written will be to fract001.gif. The
next image written is to fract002.gif unless you set OVERWRITE to yes
on the <x> screen and also enter a savename of fract001.gif.
The default for this option was set incorrectly for versions of
Fractint earlier than V15.0 and this produced unreliable results.
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PARAMS=n/n/n/n...
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The PARAMS options is used to enter from 1 to 4 parameter values to be
used during the creation of a fractal. Some fractal types do not take
any parameters at all. For several types, the four values represent
the real and imaginary parts of two complex numbers. Some types use
only the first parameter position to pass a decimal value to the
fractal formula.
To use the parameters correctly, you must know what the parameter
values mean for the particular fractal type you are creating. In Part
III of "A Guide to Fractint" you will find descriptions of each of the
ractal types and these descriptions include the parameters which that
type accepts and how they are interpreted.
The most common usage is to pass a single complex number to the
fractal formula. Usually, this identifies a location within the
complex space of a fractal. Therefore, the real number entered as the
first parameter is most likely to be within the range -1.5 to +1.5
since this applies whether the complex number is used for either the X
or the Y axis of the complex space. The second parameter is therefore
the real coefficient of the imaginary part of the complex number and
can be any real number.
In some cases, when you select the fractal type the box which comes up
does not ask for parameters, but asks instead for--
Real perturbation of Z(0)
Imaginary perturbation of Z(0)
What this is asking for is values for Params 1 and Params 2.
For example, if you use--
fractint type=julia params-0.48/0.626
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then this will show you the Julia fractal at the location (-0.48,
0.626) in the complex space. For a description of the coorinates of
this space, see the description of the CORNERS option. If you enter
parameter 1 and 2 values other than (0,0) for either a Mandelbrot or
Julia fractal then the <spacebar> toggle between M-set and J-set image
no longer works.
For Julia and Mandelbrot fractals, the third and fourth parameters are
used to enter the complex value for the c coefficient. This
coefficient is defined in the description of the FORMULA options.
An example in which the parameters are not one or two complex values
is the single parameter used by the newton and newtbasin fractal
types, thus if you use--
fractint type=newtbasin params=7
then the resulting fractal will have a 7-fold symmetry.
The "classical" Mandelbrot (which is Fractint's default image) can
also be created with--
fractint type=manzpower params=0/0/2
and the quartic Mandelbrot can be created with--
fractint type=manzpower params=0/0/4
The PARAMS option is used to set the parameter values from outside of
Fractint--i.e. for use in batch mode or when executing Fractint at the
command line. They can also be changed from within Fractint.
The bifurcation fractal type is an example of one in which the
parameter value is a single decimal code, thus--
fractint type=bifurcation params=1
produces an "unfiltered" image. 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.
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For many fractal types, when you press <t> to obtain the list of
fractal types, select a type, and press <Enter> then a box will come
up which displays the default values for the four parameters and
allows you to change these. You can enter pretty much any parameter
values you want. In some cases the image you get can be null--all
solid blue with no nothing. In some cases, you'll get what appears to
be a degenerate Mandelbrot, with just a couple of colored pixel blocks
and broad swaths of color bands. Actually, this last kind is
sometimes worth investigating--for example by turning decomposition
on--even though the initial, degenerate image is boring. No matter
what combination of numeric values you enter as parameters, it is
highly unlikely that you will crash Fractint.
For some fractal types, even a small difference in parameter values
can produce a very different image. By small, is meant the difference
between entering 1.3333295 and entering 1.3333296. For other fractal
types, all entered parameter values produce exactly the same result
(usually because that fractal type doesn't use the parameter at all).
An example is the Marksmandel fractal type, in which PARAMS=0/0/4 and
PARAMS=0/0/5 produce quite different results. You can also enter a
complex value in the first two parameter positions to create a warped
marksmandel fractal.
When you press the <tab> key, the information display shows you the
parameter values for the current image.
One useful feature of the parameters is that they do not change
between starting one fractal and starting another if they are of the
same type. Thus, you can select the type, set the parameters, and
view the image. Then you can press <t> again and when the parameter
box comes up it will show the same parameters which you set the first
time. You may wish to use the same parameters, but turn decomposition
on. You may wish to change one of the parameters a little bit and
viewing the result. At any rate, it's a convenient feature.
In the description of the FORMULA options, the terms P1 and P2 are
used since these are user-enterable parameters used in the definition
of fractal formulas. Both of these are complex numbers and the
correspondence is:
P1 = (Params1, Params2)
P2 = (Params3, Params4)
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PASSES=1|2|g|b
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
By default, Fractint makes several passes over the image when creating
a fractal. On the first pass the color appears in large, chunky
blocks. On the next pass these are broken into smaller blocks, which
are in turn broken down yet smaller on the next pass.
One purpose for this is that the first pass can be done rather
quickly, which lets you see the overall structure of the image. If
you are using the <v> key to reduce the total image size then you can
look at the general structure quite quickly.
If the first pass looks okay, then you can let the second, third, and
fourth passes occur. Each pass takes as long as all of the previous
passes to finish. The total number of passes it takes is determined
by the <videomode> selected. For an EGA monitor, two passes may be
enough. For a VGA monitor, three passes are usually made. For SVGA
and higher resolutions, four passes are made.
You can specify that Fractint take only one pass. This single pass
may take a fair while to develop, but the total time will be less than
for three (or four) separate passes. Because a single pass is slow,
you will not be able to get an idea of the looks of the fractal until
it has drawn about half of the screen. Similarly, you can force
Fractint to use two passes. The development time is the same for
either one or two passes.
The default value for the PASSES option is "g" which represents the
word "guessing". This tells Fractint to make its best guess at how
many passes are needed to complete the image. For most purposes, you
need never change this value.
However, the one exception (a purpose for which you would want to
change it) is to use the Boundary Tracing feature. This feature is
used by specifying--
fractint passes=b
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on the command line, or by pressing the <x> key and changing the code
for the first line of the parameter box, which is--
Passes (1, 2, g[uessing], or b[oundary trace])
to a "b" from its default value of "g".
Which ever way you change it, the result is that Fractint uses a
boundary tracing algorithm to draw the fractal image. This uses a
completely different way of painting the image. It uses only one
pass. The program identifies enclosed blocks of color and fills in
the entire block in one swell foop. To see what this means, try using
this option with the default Mandelbrot.
Boundary Tracing works only 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.
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.
You should set PASSES to either 1 or 2 before viewing orbits by
pressing the <o> key while a fractal image is developing because the
default "g" solid-guessing algorithm suppresses the display of some of
the most interesting orbits.
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PERIODICITY=no|show|nnn|-nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used to control periodicity checking. The default
value of "no" turns it off.
Entering PERIODICITY=show lets you see which pixels are painted the
inside color due to being caught by periodicity. If you use:
fractint type=mandel periodicity=show inside=0
then the M-set will have a black lake which is filled with a pattern
of blue blocks. The blocks get smaller on each pass, but still remain
after the last pass.
Entering--
fractint type=mandel periodicity=2
will specify use of a more conservative periodicity check. Each
increase by 1 in the value divides the test tolerance by 2. To see
the difference, press the <o> key to make orbits visible while the
image is developing.
Entering a negative value, such as--
fracting type=julia periodicty=-4
both changes the periodicty check and also turns on the show option.
For speed purposes, Fractint turns the 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). A loop becomes periodic when
it begins turning out the same result for each successive iteration
and would continue to do so until the maximum iteration value is
reached.
Periodicity checking is most important in calculating the points on
the inside (i.e. in the lake and its tendrils) because iteration of
the formula for inside points will always go to the iteration limit.
Thus, if you set MAXITER=1000 and the formula starts producing the
same result after the tenth iteration then you save 990 unnecessary
time-consuming iterations if you exit when periodicity begins. High
iterations are often needed to bring out detail along the shoreline.
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PERSPECTIVE=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used to set the distance the viewer position is away
from a 3D fractal.
The term "aspect" refers to the way in which a 3D image appears as a
result of the current axes, angles, and viewpoint. It is concerned
only with the geometric relationships, not the colors or particular
fractal pattern.
The aspect of a 3D fractal is a function of four values. These are:
x angle of x axis
y angle of y axis
z height of z axis
p distance to viewpoint
By manipulating these four values you can view the 3D fractal from any
angle around, under, over, or behind the fractal.
There are two related coordinate systems which apply to 3D fractals.
The first is the x,y,z axes of the fractal itself. The second is the
x,y,z axes of the viewpoint from which the fractal is seen. For
example, if you are holding a book in your hand you can change its
aspect by either rotating the book or by moving your body so that you
are viewing the book from a different perspective. You can move the
book, you can move your eyes, or you can do both.
The PERSPECTIVE option is equivalent to observing a book by moving
your eyes closer or further from the book in a straight line. You
don't move around the book, simply towards or away from it. Thus, you
are defining the distance between your viewpoint and the object you
are viewing.
The default value is PERSPECTIVE=0 in which the perspective
calculations are turned off. The three axes of the fractal will not
be displayed as if viewed from a perspective. Calculation of the
fractal image is faster if the perspective computations are turned
off.
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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 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.
The maximum value you can use is 999.
With the Lorenz attractors, setting PERSPECTIVE=100 or less will get
you inside of the orbits. This is also a good place to turn the
SOUND=x option on.
See also: SHIFT, XYSHIFT
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POTENTIAL=maxcolor[/slope[/modulus[/16bit]]]
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Enables the "continuous potential" coloring mode for all fractal types
except plasma clouds, IFS and IFS3D. Note that if you import a GIF
file not created by Fractint then it is read in as a plasma cloud.
This option can be used with 256-color modes only.
The four arguments define:
the maximum color value MAXCOLOR
the slope of the potential curve SLOPE
the modulus "bailout" value MODULUS
the 16-bit off/on flag 16BIT
An example of usage is: POTENTIAL=240/2000/40/16bit
These parameters may be changed on the <y> Extended Options and
Doodads screen.
You may omit arguments from the rightside in, thus POTENTIAL=200/1500
will set the maximum color value to 200 and the slope of the potential
curve to 1500. The modulus "bailout" value will default as will the
16bit flag. For that flag, the default is OFF. The Mandelbrot and
Julia fractal types ignore any modulus "bailout" value you enter and
always use a hardcoded value of 4.
MAXCOLOR
This is the color corresponding to zero potential, which plots
as the TOP of the fractal.
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.
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SLOPE
Slope affects how rapidly the colors change -- the slope of
the "mountains" created in 3D.
If the slope is too low, the palette will not 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
This 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.
You must have floating point turned on to use MODULUS values
higher than 127. If floating point is not the default for the
fractal type you are using, the FLOAT option may be used to
turn it on (or you can do so on the <x> Options and Doodads
screen). If you enter a value higher than 127 while using
integer arithmetic, the value will be truncated down to 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 to each
stored pixel, for a much smoother result when transforming to
3D. This also appreciably enlarges the size of the file which
contains the image.
Fractint's visible behavior is unchanged when 16BIT is
enabled, except that solid guessing and boundary tracing
options are not used.
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When you save an image generated with 16BIT continuous
potential the extension used for the image file will be POT
rather than the standard GIF. Technically, the POT file is
still a GIF file but with a double-width image. If you try to
view a POT file with any GIF viewer (other than Fractint
itself, of course) then the image will be double-width.
A 16-bit POTfile 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 POTENTIAL option may be used to create the famous "MtMand"
fractal, as follows:
TYPE=mandel
CORNERS=-0.19920/-0.11/1.0/1.06707
INSIDE=255
MAXITER=255
POTENTIAL=255/2000/1000/16bit
PASSES=1
FLOAT=y
This fractal takes a while to develop. A long while, actually.
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PREVIEW=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This turns the preview option on from the command line. The result is
that the fractal image comes up in a window of reduced size. Normally
you would set this option from inside Fractint by pressing the <v>
key. It is the first choice on the Viewing Parameters screen.
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PRINTER=type[/resolution[/port#]]
PRINTFILE=filename
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
From within Fractint, you can press the <p> key to print the current
image. You must have already told Fractint what kind of printer you
have. This can be done on the DOS command line with the PRINTER
option.
Thus, to print on an Hewlett-Packard LaserJet you must execute
Fractint with the DOS command line--
fractint printer=hp
You can also put the PRINTER option in your @set file or in your
SSTOOLS.ini file. For details, see the description of SSTOOLS in this
manual.
The arguments of the PRINTER option are:
TYPE
The type argument is a code which indicates the type of
printer, these codes are:
hp = HP LaserJet
ib = IBM Graphics
ep = Epson
co = Star color printer (Epson compatible??)
pa = HP Paintjet color printer
po = PostScript SWT
ps = PostScript SWT
hl = PostScript
Within the Fractint code the printers are assigned a Printer
Type numeric value which is used to determine the default
resolution for that printer.
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The Printer Type numeric codes are given in column one and the
Printer Type alphabetic arguments are given in column two of
the following table:
Printer Type Printer Type Argument
------------ ---------------------
1 hp
2 ib
2 ep
3 co
4 pa
5 po
5 ps
6 hl
For each of the numeric Printer Types, the default resolution
is:
Printer Type Default Resolution
------------ -------------------------------
1 75 dpi
2 60 dpi
3 60 dpi
4 60 dpi
5 150 dpi
6 150 dpi
RESOLUTION
This is the number of dots per inch for the printer. Accepted
values are:
60 -- Epson/IBM (default)
120 -- Epson/IBM
240 -- Epson/IBM
75 -- LaserJet
100 -- LaserJet
150 -- LaserJet
300 -- LaserJet
90 -- PaintJet
180 -- PaintJet
10 to 600 -- PostScript
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Resolution is set internally within Fractint depending upon
screen resolution. For example, an image with 600 lines will
print with 100 lines on a LaserJet printer. If the image has
more than 800 lines it will print with 150 lines on the
LaserJet.
For the IBM, Epson, and Star printers the breakpoints are
different. If the image has more than 480 lines (but fewer
than 960) then 120 lines will be used on the printer.
LaserJet
Pixels Dots
<600 75
>600 100
>800 150
>1200 300
IBM/Epson/Star
Pixels Dots
<480 60
>480 120
>960 240
PaintJet
Res Used
<150 90
>150 180
PostScript
Pixels Dots
<10 10
>600 600
600 600
n n (always 1:1 pixel to printer dot)
For the PaintJet, if the resolution requested is less than 150
then a resolution of 90 will be used. If the requested
resolution is greater than 150 then 120 will be used.
The PostScript printer can print a 1:1 relationship between
screen pixels and printer dots up to a maximum of 600.
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PORT
Acceptable port values are:
1 -- for LPT1 (default)
2 -- for LPT2
3 -- for LPT3
11 -- for COM1
12 -- for COM2
13 -- for COM3
14 -- for COM4
-1 -- write to file (PostScript only)
If you have a PostScript printer and use a negative number for
the port argument then the printout will go to a file named
fract001.prn. This name will be incremented in the usual
fashion as you create other printer files. You can also
specify the name to be used with the PRINTFILE= option.
See also the description of the COMPORT option.
"Disk video" modes can be used to generate images for printing at
higher resolutions than your screen supports.
VIEWING WINDOW 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 does not preserve
aspect ratio with printers other than PostScript.
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To maintain a correct aspect ratio on non-Postscript printers, use the
following procedure to create a high-resolution "disk video" mode
image file:
o set <v> Viewing Window parameters:
preview to yes
reduction to 2
aspect ratio to 1.6
crop to yes
o display the image to be printed
o set preview display back to no
o start final calculation in a high resolution "disk video" mode
o print directly to a PostScript printer, or save the result as a
GIF file and use external utilities to convert to hard copy.
See also: COMPORT, TITLE, EPSF, TRANSLATE, HALFTONE, DISTEST
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RADIUS=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This controls the radius of a spherical fractal. It controls the
overall size of the globe.
To set it from within Fractint:
a. press <3> to get 3D Mode Selection screen
b. select Spherical Projection by entering "yes"
c. enter radius value
You enter the radius value on the Sphere 3D Parameters screen on the
line which says--
Radius scaling factor in pct
The default value is 100. Smaller values will make the sphere appear
smaller.
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RANDOMIZE=n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option smooths the transition between colors of a 3D fractal by
randomly varying the color of a pixel to those of nearby colors. This
minimizes map banding. In 3D transformations banding tends to occur
because all pixels of a given height end up the same color. The
RANDOMIZE option is usable with all FILLTYPES.
The argument, n, may be from 0 to 7. A value of zero disables this
feature and this is also the default. A value of 7 randomizes the
hell out of the colors. For a reasonable degree of randomization, try
a value of 3.
This value may be set inside Fractint on the Planar 3D Parameters
screen, obtained by pressing the <3> key. The prompt there is--
Randomize colors (0-7, '0' disables)
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ROTATION=xrot[/yrot[/zrot]]
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option rotates a 3D fractal image.
As mentioned in the description of the PERSPECTIVE and SHIFT options,
you can change the view of the fractal by either rotating the fractal
itself or by moving your viewpoint around the fractal. The end result
can appear to be the same, the difference being only whether you move
you or you move it. You can, if you wish, both rotate the fractal and
move the viewpoint--although this could quickly become geometrically
confusing.
If the fractal type does not support rotation then nothing will happen
when you try it.
You can set the ROTATION values from inside Fractint by pressing the
<i> key, which will bring up the 3D Parameters screen. You can also
set it by pressing <3> and getting the Planar 3D Parameters screen.
The default setting is ROTATION=60/30/0.
Perhaps the easiest way to visualize the effects of ROTATION and
similar geometric options is to first bring up a GIF file which has an
easily-identifiable geometry--such as a human face. Use this to make
a 3D fractal and then rotate, shift, translate, and otherwise
manipulate the image. No matter how much you distort it, the image
and its geometry will still be recognizable. When you are
manipulating a fractal image, it is fairly easy to lose track of where
you are in relation to the three axes. If you do use a fractal image,
the Gingerbreadman fractal has a shape which is most easy to follow
during geometric transformations.
The X value tilts the bottom of the image towards you by X degrees,
the Y value pulls the left side of the image 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) image. All rotations actually occur
through the center of the original image.
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ROUGHNESS=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
See the description of the SCALEXYZ option. The ROUGHNESS option
scales the Z axis.
The nn argument is a percentage. Negative percentages are allowed--
for example, for the M-set setting ROUGHNESS=-30 will place the lake
"below" ground. Naturally, this option applies only to 3D fractals,
since 2D fractals do not have a visible Z axis, except for the colors.
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RSEED=nnnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The option unrandomizes the randomness of plasma clouds. This lets
you repeat the same plasma cloud. Normally, the seed used in creating
a random number is derived from the current time. By using RSEED you
are overriding this and setting the seed to a known value. Since the
value is known, you can repeat it.
The seed value is shown on the <tab> display.
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SAVENAME=name
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option defines the name which will be used when a fractal image
is saved to a GIF file. The default name is FRACTnnn.GIF in which nnn
is initially 001 and automatically increments to the next number if
the number already exists.
If you enter a savename such as MYNAME then this is taken to be
MYNAMEnn.GIF thus the first GIF file saved is named MYNAME1, the next
one is MYNAME2, and so forth.
You can set this from inside Fractint on the <x> Options and Doodads
screen.
It is also useful to set this when creating a fractal in batch mode,
for example:
fractint filename=oldfract savename=newfract batch=y
See the description of the BATCH option for an explanation of this
command line.
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SAVETIME=nnn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Assuming that you are creating an image in BATCH mode which takes a
long time to develop, you can specify that automatic saves be
performed at regular intervals, thus:
fractint myfract savetime=30 batch=y
This will automatically save the file to fract001 every 30 minutes.
The same filename will be used over and over again. If you also
specify the filename, as in:
fractint myfract savename=newname savetime=60 batch=y
then the save will be to the newname.gif file every 60 minutes.
See also: BATCH
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SCALEZYZ=nn/nn/nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option scales the light when using the LIGHTSOURCE option to
create a Targa fractal.
For example, SCALEXYZ=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, SCALEXYZ=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.
If you use SCALEXYZ=90/90/30 then 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.
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.
See also: LIGHTSOURCE, AMBIENT, 3D
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@SET
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This is not an option but represents the name of a file which contains
options. If this file is referenced on the command line then the
commands in the file are included. For example--
fractint @set
If the contents of the file named "set" is--
video=Alt-9 textsafe=yes inside=0 askvideo=no
then this is as if you had entered--
fractint video=Alt-9 textsafe=yes inside=0 askvideo=no
The name "set" is not required. You can name this file anything which
is acceptable to DOS. You can include more than one option file on
the same command line, for example--
fractint @set @colors
which includes the contents of two files both of which contain option
settings.
However, there is one special option filename. If you name the file
which contains the options SSTOOLS.INI then you do not have to
reference it on the command line. Fractint acts as if you had
entered:
fractint @sstools.ini
when you use the command:
fractint
Thus, by default Fractint reads the contents of a file named
SSTOOLS.INI and appends the options in the file to the command line.
This file can be anywhere along your path--it need not be in the same
subdirectory as the Fractint executable file.
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SHIFT=xshift/yshift
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option moves a 3D image around the screen. For example, if you
create a sphere then, by default, it appears in the middle of the
screen. If you define SHIFT=20 then the sphere will appear on the
right side of the screen; use SHIFt=-20 and it is on the left.
If you use SHIFT=20/20 then the image will be in the upper left corner
of the screen. You get the idea. A value of about +/-50 will cause
the image to be shifted complete off the screen.
You can shift the image from inside Fractint on the Planar 3D
Parameters screen, where the prompts are--
Image non-perspective X adjust (positive=right)
Image non-perspective Y adjust (positive=up)
The SHIFT option shifts the image *without* any perspective
adjustments. The XYSHIFT option is used to shift *with* perspective.
Normally, perspective is defined so that the image appears in proper
perspective when viewed from the very center of the screen. If you
shift its location and also maintain perspective then it appears at
the new location and the perspective is correct as seen from the
center of the screen. If you shift its location and do not maintain
perspective then the image is shifted but the point from which the
perspective is correct is still directly above the image location on
the screen, not the center of the screen. In other words, the
perspective location also moves along with the image.
Another way of putting this is that SHIFT moves the image *before*
applying perspective and XYSHIFT moves the image *after* applying
perspective.
See also: XYSHIFT, XYADJUST, PERSPECTIVE
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SMOOTHING=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used when creating Targa LIGHTSOURCE images. It
smooths the effect of the light hitting the fractal. It reduces
granularity. It sets the average light level.
Setting SMOOTHING=2 is a reasonable value to start with. A value of
2 or 3 will allow you to see the large shapes better.
This is primarily useful when doing light source fill types with
plasma clouds. 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 option is therefore
useful if you are using a plasma cloud fractal which was derived by
importing a GIF file.
If you are using continuous POTENTIAL then you do not need this
option.
This option may be set from inside Fractint by choosing "light source
after transformation" on the 3d menu. The Light Source Parameters box
will appear. One of the items on it is:
Light Source Smoothing Factor
the default value is 0.
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SOUND=off|x|y|z
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option works only with the attractor fractal types (such as
Lorenz) and you should also have FLOAT turned on.
As one might expect, the result is sounds through your computer's
speaker. Sound boards are not supported. This option produces what
is basically fractal noise, not music. Well, not what most people
would call music anyway. Listen for yourself.
You can control whether a sound is created by changes in any of the
three axes. Thus, SOUND=x will produce a sound in response to x-axis
events.
The default is SOUND=off. Thank goodness.
You can control the tone of the noise made with the HERTZ option.
You can set this option from inside Fractint on the <x> Basic Options
screen. The prompt there is--
Sound (no, yes, x, y ,z)
The default setting is "yes".
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SPHERE=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option can be set from inside Fractint by pressing <3> and
obtaining the 3D xxxx screen. One of the prompts is "Sphere". The
default is NO. Change it to YES and a spherical 3D image will be
created.
You can change the size of the sphere with the RADIUS option.
The following options and defaults apply to spherical fractals:
Option Default
----------- -------
LATITUDE 180/0
LONGITUDE -90/90
RADIUS 100
ROUGH 30
WATERLINE 0
FILLTYPE 2
PERSPECTIVE 0
XSHIFT 0 (w/perspective)
YSHIFT 0
XADJUST 0 (w/o perspective)
YADJUST 0
LIGHTSOURCE 1/1/1
SMOOTHING 0
AMBIENT 20
RANDOMIZE 0
HAZE 0
FULLCOLOR 0
See also: LATITUDE, LONGITUDE, RADIUS
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STEREO=n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used to select the type of stereo image creation.
The argument, n, may be 1, 2, or 3. These values mean:
0= normal 3D image
1= red/blue created with 64 shades of gray
2= red/blue created with 16 shades of gray
3= full color
Each of these requires certain equipment to view. Option 0 requires a
pair of eyes. Options 2 and 3 require a pair of red/blue funny
glasses. Option 3 requires specialized equipment.
The difference between Option 1 and 2 is that 1 is intended for use
with VGA monitors and 2 is intended for use on EGA monitors. Option 2
also works fine with wire-frame images, lorenz3d fractals, and ifs3d
fractals, none of which require more than 16 colors to look good.
When you set STEREO=3 then the left image presented on the screen
first. You may photograph it or save it. Next, the second image is
presented. You can then take the two images and convert them to a
stereo image pair.
For example, you can capture the images with a Matrix 3000 film
recorder -- which is 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, including Kodak Ektachrome 64 daylight for slides and a few
print films. The film chips are then glass-mounted. 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 requires mounting the chips using the
7-sprocket Busch-European Emde masks.
Because both a red and a blue pixel are created for each point on the
image, the resolution is effectively halved. The minimum usable
resolution to use is 640x350.
Generally glasses1.map is designed for use with STEREO=1 (alternating
pixels), and glasses2.map is for STEREO=2 (superimposed pixels).
Grid.map is great for wire-frame images using 16 color modes.
See also: INTEROCULAR, CROP, CONVERGENCE, BRIGHTNESS
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SYMMETRY=xxx
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Here, the "xxx" may be:
none
xaxis
yaxis
xyaxis
origin
pi
You must enter all of the letters of the argument, not just the first
letter. Thus, if you want symmetry about the origin, you must enter:
SYMMETRY=origin
The symmetry normally defaults to that defined for each type of
fractal or formula.
You cannot set the SYMMETRY from inside Fractint. This option is
usually used by formula developers during debugging.
For information about each of these symmetries, see the description of
the FORMULAFILE option.
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TEXTCOLORS=aa/bb/cc/...
TEXTCOLORS=mono
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option affects the colors in which Fractint's menus, parameter
boxes, error message boxes and the like appear on a color monitor.
If you wish, you can change any of these colors. However, there is
little (if no) reason to do so.
The argument aa/bb/cc... represents the 27 values which are part of
this argument. You can set a single value individually, for example:
TEXTCOLORS=////43
Sets the fifth value to 43 and leaves the first four values at their
defaults.
Each of the values is a two-digit number. The arrangement is:
digit 1 = background color (0 to 7)
digit 2 = foreground color (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
Only the colors and values in the left column may be used for the
background. Colors from either column may be used for the foreground.
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The default is--
VALUES GROUP POSITIONS
------------------------ ------------- ---------
textcolors=1F/1A/ SCREEN HEADER 1-2
2E/70/28/ HELP 3-5
78/17/1F/1E/2F/5F/07/0D/ MAIN MENU 6-13
71/70/78/0F GENERAL 14-17
/70/0E/0F/ DISK VIDEO 18-20
4F/20/ DIAGNOSTICS 21-22
17/20/28/0F/07 CREDITS 23-27
In real use, all of the arguments must be on one line together. The
comments in the option above show you groups within the 27 values.
Thus Values 1 and 2 define the colors for the screen header, which is
a one-line message at the top of the screen and which displays the
Version Number of the program.
The Help Screen colors are defined by the values in positions 3, 4,
and 5. The meanings of each of these positions is given in the table
below:
****** screen header ******
POS
1 Fractint version info
2 not used
****** help *******
3 sub-heading
4 main text
5 instructions at bottom of screen
****** Main Menu ******
(also selection boxes and 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
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****** 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
For example, you can change the background around the Main Menu. This
is Position 6 and the default value is 78 (white background; gray
foreground) to the value 2D (green background; light magenta
foreground) with--
TEXTCOLORS= /////2D
You cannot change the colors from inside of Fractint. In fact, if you
do change the colors you probably want to use a @SET file or the
SSTOOLS.INI file so that the changes are, in effect, permanent.
If you create a new color appearance for Fractint which is
aesthetically pleasing, would it be possible for you to share the
TEXTCOLORS option you use by leaving a message on CompuServe, in
Library 15 of the COMART forum? Thank you.
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TEXTSAFE=y|n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
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=n",
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.
Try using this option if you are having trouble bringing Fractint up
properly on your system.
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3D=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Three-dimensional fractals are one of the most fascinating and complex
aspects of Fractint. To explore the subject thoroughly would take
another manual the size of this one.
At least three different general reasons for creating a 3D fractal
exist, thus:
a. to explore fractal geometry
b. to create exciting images
c. to enjoy oneself
In any case, the key to producing a really good 3D fractal is
planning. It takes care and patience to create a truly elegant image.
Start by doing the default 3D form of the Mandelbrot fractal. This
one is good for learning to manipulate the geometry. It is a fast-
developing fractal and it is easy to recognize its orientation no
matter how it is rotated or transformed. Practice moving the entire
fractal around the screen. Try different viewer perspectives.
Next, do a straight 3D image of a spiral detail from a Julia fractal
and try it with the different FILLTYPEs.
Try creating a spherical image by pressing the <3> keys and following
the prompts. Again, practice moving the fractal globe around the
screen and altering its diameter. Try different maps. Some rather
interesting spherical fractals can be made by starting on a GIF file.
If the GIF is of the face of a horse then this will be turned into a
sphere (which looks kinda neat, actually). Incidentally, while you
have the horse GIF on the screen you should press <e> to bring up the
Palette Editor and then <s> to save the palette. Since the palette is
based upon the colors of a horse's head it has a nice organic
combination of colors. Colormaps which are derived from GIFs are
almost always interesting (and often surprising). You can also color-
cycle ordinary GIF files which sometimes awful and sometimes
interesting results. If you do this you should slow the cycling rate
way down with the <down arrow> key. The GIF is read in as a plasma
fractal and the cycling rate for plasmas is, by default, set to the
maximum speed.
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While we've wandered of the main subject here, it is worth mentioning
that Fractint makes an excelllent GIF viewer. In fact, it makes a
superb GIF viewer. It will load any GIF87a or GIF89a image which your
system is capable of displaying and simply display it. When you
press the <r> key you get a list of the GIF files in the current
directory. You also get a list of all of the subdirectores. Thus, it
is easy to keep your GIFs in separate subdirectories. One possible
arrangement of subdirectories is:
Volume in drive C is unlabeled
Directory of c:\fraint\*.*
. <DIR> 1-07-91 14:59
.. <DIR> 1-07-91 14:59
fractint.exe 392862 12-21-90 16:09
fractint.frm 8732 1-14-91 22:38
fractint.l 5772 12-09-90 1:10
sstools.ini 62 1-20-91 20:37
ADULT <DIR> 2-02-91 8:17
IFS <DIR> 1-07-91 15:02
FRACTALS <DIR> 12-22-91 17:40
MAPS <DIR> 1-07-91 15:01
PICTURES <DIR> 1-31-91 21:41
579,584 bytes in 25 file(s)
43,727,360 bytes free
Here, all of the IFS files are kept in the IFS subdirectory. All
colormaps are in the MAP directory. The PICTURES directory contains
GIF images of mountains, horses, cars, and so forth. The ADULT
directory contains other pictures. The FRACTALS directory contains
GIF files created by Fractint.
The speedkey feature also helps with this subdirectory structure. For
example, you can setup Fractint so that as soon as it comes up it
starts drawing the default Mandelbrot. As soon as it starts you can
press <r><p><Enter> quickly and the list of the GIFs in the PICTURE
directory will be displayed. Similarly, entering <r><f><Enter> will
bring up the list of fractal image files.
One special kind of 3D image is the overlay. You can overlay any
smaller GIF file on a larger one. The overlay will be drawn using 3D
dimensionality. By default, 3D images are tilted to 60 and 30 degrees
from the axes. If you set the axes to 90 and 0 then the image will
appear in its regular 2D appearance. Once you have overlayed one
image on top of another you save the result. This result can be used
as the base upon which another 3D image is overlayed. This can be
continued. You can, for example, create an image with seven fractal
globes on it.
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The image has only one colormap file and when you overlay one image on
top of another the default colormap is used. Wait until the combined
image is complete and then load a different colormap. Thus, if you
start with a picture of a truck and overlay with a fractal globe then
the colors in the truck GIF will become distorted because of the
effects of the default.map. When the image is complete, re-load the
truck.map file (which you saved earlier, right?).
At some point you must consider what you plan to do with the final
image. You follow one path if your intent is to create a printout of
a fractal on a laser printer. A very different set of options would
be used if you plan to create a static (i.e. not color-cycling) screen
image. In this case, you would probably use the Palette Editor to
create a special palette--as opposed to a palette which is designed to
be good at color-cycling. The techniques needed are quite different.
The following options and defaults apply to non-spherical 3d fractals:
Option Default
----------- -------
ROTATION 60/30/0
XSCALE 90
YSCALE 90
ROUGH 30
WATERLINE 0
FILLTYPE 0 or 2
PERSPECTIVE 0
XSHIFT 0
YSHIFT 0
XADJUST 0
YADJUST 0
LIGHTSOURCE 1/-1/1
SMOOTHING 0
AMBIENT 20
RANDOMIZE 0
HAZE 0
FULLCOLOR 0
TRANSPARENT 0
See also: SPHERE
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TITLE=y
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
If specified, title information is added to printouts.
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TRANSLATE=y|-n|n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
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. Note that the
"n" here is an integer number, not the letter "n".
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TRANSPARENT=min/max
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option defines a range of colors to be treated as "transparent"
when <O>verlaying 3D images.
Thus, if you enter TRANSPARENT=100/150 then all of the colors numbered
100 to 150 of the map of the overlay file will become transparent.
Where these colors would be you can see through to the fractal below.
Actually, the transparent colors allow you to see through the fractal
to whatever is on the screen below.
It takes a bit of planning (or pure luck) to use this option
effectively, but with it you can create highly unique and unusual
images of combined fractals.
This option can also be set from within Fractint when you press the
<o> key to begin adding an overlay file.
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TYPE=typename
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
On the Main Menu is the choice--
Select fractal type <t>
When you select this choice (or when you press the <t> key) a list of
the available fractal types will be displayed. The exact list you get
depends upon the version of Fractint you have. Some of the types
listed are families--if you select one of these you will get another
list of the fractal types within that family. Examples of this
fractal type are those named "formula" or "l-system".
You can select a fractal type by moving the highlight to your choice
and pressing <Enter>. You can also use a speed key. Thus, if you
press the <p> key then the highlight will move to the first type with
a name beginning with this letter. If you enter <p><a> then the
highlight moves to the first name beginning with "pa".
After you select the fractal type, you will usually get a parameter
box in which you can enter values for the parameters which can be set
for that fractal type. This list of parameter values differs for
different fractal types. You can always accept the default
parameters--an entry within this box is not required.
When you press the <b> key to write out a command line to the
frabatch.bat file it always writes out a TYPE= option for the current
fractal type.
For information about each of the individual fractal types, see Part
III of this Guide to Fractint.
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VIDEO=xxx
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The "xxx" argument is a Videomode Identifier. These are generally the
names of the key combination which can be pressed to select that
videomode. For example, one of the videomodes is:
SF5 640x480x256 SVGA
The "SF5" means that pressing <Shift>-<F5> will change to this SVGA
video mode. You can also select the videomode on the command line,
thus--
fractint video=SF5
However, just because SF5 means 640x480x256 now doesn't mean that it
will mean that forever. In fact, the list of videomodes changes for
every version of Fractint. Furthermore, you can customize the list
yourself with very little effort by using the BATCH=CONFIG option.
You can change the videomode from inside Fractint by returning to the
Main Menu and selecting the "Select Video Mode" screen. A scrolling
list of all of the available modes will appear. Whether you are on
this list or not, you can select a videomode by pressing the
associated keys. Thus, if you have an image on the screen and press
<Shift>-<F5> then the image will be redrawn at the 640x480 resolution
(unless of course, it's already at that resolution, in which case
nothing happens).
Normally, when you load an image from an external file, Fractint will
present a message showing you the resolution of the incoming file and
asking you to verify that this resolution is okay for your monitor.
You can suppress this question with the ASKVIDEO option.
You can set your own default videomode in one of two ways. You can
put a VIDEO=SF5 option (with "SF5" replaced by the mode you want to
set as the default) in your SSTOOLS.INI file or in a @SET file.
Another way to set your own videomode default is to use BATCH=config
and then edit the fractint.cfg file so that your choice is listed as
videomode F3. Unless you specify otherwise, Fractint will use the
mode represented by F3 as the default.
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WARN=y|n
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
WARN=y prevents over-writing old .GIF files with the same name. This
is the default. Setting WARN=n will change this and allow overwriting
without a warning message.
The defaults for filename creation are now set correctly by Fractint
(they were confusing for versions earler than V15.0) thus this option
isn't really needed anymore.
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WATERLINE=nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
This option is used only for 3D fractals. The argument, nn, is a
color number. All colors nn and below will be the "inside" color.
Thus, if you use--
fractint WATERLINE=12 INSIDE=0 FILENAME=MYFILE 3D=y
Then the lake will be larger and push up over where the shore used to
be. The colors from the shoreline out are numbers 1,2,3,4,5, and so
forth.
This option can be used to fill in valleys and turn them into lakes.
You can create your own Lake Powell.
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XYADJUST=nn/nn
XYSHIFT=nn/nn
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
XYADJUST=nn/nn shift image in the x/y dir *without* perspective
XYSHIFT=nn/nn Shift image in x/y dir *with* perspective
See also: PERSPECTIVE, SHIFT, ADJUST
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