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FracTrace/!FracTrace/FTS-Def
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Micro User » MU 1991-09.adf » PD-Stuff |
| Filename: | FracTrace/!FracTrace/FTS-Def |
| Read OK: | ✔ |
| File size: | 3D9E bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
FracTrace Script (FTS) command descriptions
-------------------------------------------
An FTS file is a plain ASCII text file containing the commands and their
right parameters to describe a fractal surface and its rendering in
FracTrace.
Lines may contain : - a single command
- multiple commands, separated by a semi-colon ';'
- comments, preceded by a back-slash '\'
- the combination of both commands and comments
Some good examples of FTS files can be found in the 'FTS-Files' directory.
A description of each individual command follows underneath:
Command Description
-----------------------------------------------------------------------------
Title Sets the title for the current surface(s). This title is
used for all file-handling. A string of maximum eight
characters is given as the sole parameter.
Example: Title Snowy
Frames Sets the maximum number of 'frames'. The parameter is an
integer.
Example: Frames 24
Scope Sets the range of frames to be rendered. If you have set
the maximum number of frames to, say 24, it is possible
to set the range of frames to be rendered to any
interval within 1..24. The two parameters are the
minimum and maximum frame number.
Example: Scope 3,18
Mandelbrot Tells the program that the set to be used is the
Mandelbrot Set. This command takes no parameters.
Julia Tells the program that the set to be used is a Julia
Set. This command takes no parameters.
Resolution Sets the resolution of the surface to be calculated and/
or rendered. The units for this resolution may be
regarded as pixels. The two parameters are the x and y
resolution of the surface.
Example: Resolution 300,300
Range Sets the range in the complex plane for the part of the
set that is to be calculated and/or rendered. The four
parameters are minimum x, maximum x (real axis), minimum
y, maximum y (imaginary axis). These values can best be
obtained from a normal Mandelbrot plotting program!
Example: Range -1.5,1.5,-1.5,1.5
Cval Sets the real and imaginary part of the point to
calculate and/or render the Julia Set of. The two
parameters are the real and imaginary part of the point.
Example: Cval 0.32,0.043
Smoothness Sets the smoothness of the surface. The higher the
smoothness-value, the smoother the surface, and the more
calculations will be performed to obtain the potential
of a point on the surface! The sole parameter is an
integer, which really should be at least about 100!
Example: Smoothness 120
Depth Sets the depth of the iterations in the calculation of
the potential of a point. The higher the value, the more
precise the set will be calculated, and again, the
longer it takes to calculate a point-potential. The
parameter is an integer in the range 1..127!!!
Example: Depth 100
Mountains Tells the program to render the surface as a mountain.
This command takes no parameters.
Valleys Tells the program to render the surface as a valley.
This command takes no parameters.
Light Sets the direction of the light-vector. This vector
need not be normalised. Note that this vector is the
direction of the light-rays, ie. it points away from the
light source! The three parameters are the x, y, and z
components of the vector. (z always should be negative!)
Example: Light 0.5,1,-2
Brightness Sets the brightness of the light-source. The higher the
value, the brighter the light. The sole parameter is an
integer.
Example: Brightness 78
Steepness Sets the steepness of the mountain/valley slopes. The
higher the value, the steeper the slopes. Note that the
magnitude of this value is disproportional with size of
the region indicated with the range command. The sole
parameter is an integer.
Example: Steepness 240
Dithering Sets the color-dithering factor. Because the program
only uses 16 colors to render an image (due to the 4bit
nature of mode 12), abrupt color changes on the surface
may give a non-realistic feel to the image. Therefore,
a simple technique, called random dithering, is used to
produce intermediate 'pseudo-colors', which make the
color changes seem quite continuous. A value of 1 means
no color dithering. The sole parameter is an integer.
Example: Dithering 16
Shadows Tells the program whether to calculate shadows or not.
The calculation of shadows slows down the rendering
quite drastically. The parameter is a string of the form
'On' or 'Off'.
Example: Shadows On
Interpolation Tells the program whether to interpolate values in the
horizontal direction. Interpolating doubles the time
needed for rendering an image, but it produces more
detail. An image created with interpolation off has
'mode 9' resolution, whereas images created with
interpolation on have a true 'mode 12' resolution.
The parameter is a string of the form 'On' or 'Off'.
Example: Interpolation Off
Offset Sets the two 'screen offsets' for the image. A
horizontal offset of 0 would place the image to the left
edge of the screen. A vertical offset of 0 would place
the image half way below the bottom edge of the screen.
Normally, the x (horizontal) offset should remain at 40,
and the y (vertical) offset should vary between 240 and
480, depending on the angle at which to view the
image. The two parameters are the x and y offsets.
Example: Offset 40,380
Angle Sets the viewing angles. The first value is the x angle,
a value of 0 makes you look at the image 'head-on'.
The second value is the y angle, which should be in the
range 15..90 to get a meaningful view on the image, 30
being a quite reasonable average. In the current
versions of FracTrace, the x angle is best kept at 0!
The two parameters are the x and y viewing angles.
Example: Angle 0,25
Increment Sets the x and y 'OS-Unit' increment steps when
rendering the surface. These values are both best kept
at 4!
Example: Increment 4,4
Slope Front Sets the front-slope range and steepness. For some
images it will be necessary to use this feature to avoid
the artificial cut-off of the front-most edge of the
surface. When you do have an image that seems to be
'cut off' at the front edge, you should force the front
lines down with a certain steepness-factor!
The first value is the number of front lines you want to
pull down (one line corresponds with one resolution-
unit), the second value is the factor by which you want
to enlarge the steepness. These values should be
obtained by trial and error. The two parameters are the
slope-range (in lines) and the steepness factor.
Example: Slope Front 30,5
Color Sets the overall color of the surface. This color is
specified by an RGB-vector. The components of the RGB-
vector must be in the range 0..15! In current versions
of FracTrace the vector should be 15,15,15, as there are
still some problems with the ColourTrans module. Other
values may be used, but the only way to display these
created images correctly would be by '*ScreenLoad'ing
them (ie. not with !Paint or !FracTrace itself). The
three parameters are the components of the RGB-vector.
Example: Color 15,15,15
Var Sets (declares) the names for user-variables. See the
paragraph 'Using frames' for further details on
user-variables. This command takes up to 100 parameters,
these being the names of the user-variables.
Example: Var min,max,radius
Show Shows the contents of the specified variable in the
'report' window. This command may be useful for
debugging script programs. The single parameter is the
variable-name.
Example: Show radius
Stop Immediately stops execution (ie. parsing) of an FTS
file. When you use subroutines, a 'stop' should be
put at the end of the main program, before the start
of the first subroutine!
-----------------
The best way to get to know these commands and their effects is by
experimenting with the supplied FTS files. Try changing one parameter at a
time and noticing the change in the according image(s).
Using frames
------------
FracTrace provides a simple way to generate multiple images, called frames,
from one FTS file. This is done by allowing the user to replace any
parameter by a variable or a constant expression. (The use of variables is
recommended over the use of constant expressions!)
FracTrace allows the user to declare up to 100 user-variables. Declaration
of a user-variable is as simple as including it in the so called 'var-list'
at the beginning of a 'program'. This 'var-list' is just a list of names
you choose for your variables, preceded by the 'var' command,
eg. : 'var count, loop, step, min, max', with the words after 'var'
referring to user-variable names.
These user-variables may be assigned any expression that is legal in
BASIC V!
There are also two other 'read-only' variables which the user may use in his
expressions: 'frames' and 'frame'. The variable frames is the number of
maximum frames set with the 'Frames' command. The other variable, frame, is
the current frame number which the program is processing, which of course,
is in the range 1..frames!
Most user-variables will be defined by an expression containing the frame
variable.
There are two ways of assigning an expression to a user-variable:
1) by using the form 'variable=expression(frame)'
eg. : 'radius=60*SINRAD(frame)+100'
no spaces are allowed in the expression to the right of '=' !!!
2) by using the form 'variable=expression,expression,expression,...'
eg. : 'height=12,23,34,45,56,67,78' when frames would be 7
With the second form variable 'height' will be 12 for frame=1, 23 for
frame=2, 34 for frame=3,..., and 78 for frame=7. Of course, expressions
containing the variable frame (but no spaces!!!) may also be used in the
second from!
People who know Render Bender will be familiar with this method.
Conditional command execution
-----------------------------
FracTrace also allows conditional execution of commands with the 'if .. else
.. endif' construct!
The use of this construct is as follows:
if expression
commands
.
.
else
commands
.
.
endif
Where 'expression' is again any legal BASIC V expression evaluating to TRUE
or FALSE, eg. 'frame+4 < frames' or 'xstep >= stepsize+0.2'.
Each opening 'if' must have a closing 'endif', an 'else' is optional.
The 'if .. else .. endif' constructs may be nested up to 32 levels deep!
Repeated command execution
--------------------------
a) The first loop-construct allowed in FracTrace is 'repeat .. until'.
It is used as follows:
repeat
commands
.
.
until expression
With 'expression' evaluating to TRUE or FALSE as in BASIC V,
eg. 'count > frames'.
Each opening 'repeat' must have a closing 'until'.
The 'repeat .. until' constructs may be nested up to 32 levels deep!
b) The second loop-construct allowed in FracTrace is 'for .. endfor'.
It is used as follows:
for variable=start to end by step
commands
.
.
endfor
With 'start', 'end' and 'step' legal BASIC V expressions evaluating to a
real number, eg. 'for cnt=-3 to max by 2' or 'for size=2 to 1 by -0.1',
and 'variable' the name of a user-variable.
Each opening 'for' must have a closing 'endfor'.
The 'for .. endfor' constructs may be nested up to 32 levels deep!
Execution of subroutines
------------------------
A last feature of FracTrace is the ability to execute subroutines.
Each (part of a) subroutine is marked with a label, this label is a word
preceded by a dot '.', eg. '.routine1'.
Such subroutines are called in the following way:
commands \
. \
. \
call labelname > main program
. /
. /
stop /
.labelname \
commands \
. > subroutine 'labelname'
. /
return /
As you can see, execution of a subroutine is started with a 'call' command,
and ends with a 'return' command. Therefore, each 'call' MUST have a
'return'!!!
The subroutine-calls ie. 'call .. return' may be nested up to 32 levels
deep. (That includes recursion!)
Writing programs
----------------
You will certainly have noticed from the last three paragraphs that it is
possible to build small programs using the control constructs and variables
provided by FracTrace. These programs don't have to define a fractal surface
(they may do!), they can also be used to solve whatever - small - problem!
The FTS files 'Factorial', 'Fibonacci', 'Sum50' and 'MandelPot' are some
examples of such small programs.
Carl Declerck.
00000000 46 72 61 63 54 72 61 63 65 20 53 63 72 69 70 74 |FracTrace Script| 00000010 20 28 46 54 53 29 20 63 6f 6d 6d 61 6e 64 20 64 | (FTS) command d| 00000020 65 73 63 72 69 70 74 69 6f 6e 73 0a 2d 2d 2d 2d |escriptions.----| 00000030 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| * 00000050 2d 2d 2d 2d 2d 2d 2d 0a 0a 41 6e 20 46 54 53 20 |-------..An FTS | 00000060 66 69 6c 65 20 69 73 20 61 20 70 6c 61 69 6e 20 |file is a plain | 00000070 41 53 43 49 49 20 74 65 78 74 20 66 69 6c 65 20 |ASCII text file | 00000080 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 20 63 |containing the c| 00000090 6f 6d 6d 61 6e 64 73 20 61 6e 64 20 74 68 65 69 |ommands and thei| 000000a0 72 0a 72 69 67 68 74 20 70 61 72 61 6d 65 74 65 |r.right paramete| 000000b0 72 73 20 74 6f 20 64 65 73 63 72 69 62 65 20 61 |rs to describe a| 000000c0 20 66 72 61 63 74 61 6c 20 73 75 72 66 61 63 65 | fractal surface| 000000d0 20 61 6e 64 20 69 74 73 20 72 65 6e 64 65 72 69 | and its renderi| 000000e0 6e 67 20 69 6e 20 0a 46 72 61 63 54 72 61 63 65 |ng in .FracTrace| 000000f0 2e 0a 0a 4c 69 6e 65 73 20 6d 61 79 20 63 6f 6e |...Lines may con| 00000100 74 61 69 6e 20 3a 20 2d 20 61 20 73 69 6e 67 6c |tain : - a singl| 00000110 65 20 63 6f 6d 6d 61 6e 64 0a 20 20 20 20 20 20 |e command. | 00000120 20 20 20 20 20 20 20 20 20 20 20 20 20 20 2d 20 | - | 00000130 6d 75 6c 74 69 70 6c 65 20 63 6f 6d 6d 61 6e 64 |multiple command| 00000140 73 2c 20 73 65 70 61 72 61 74 65 64 20 62 79 20 |s, separated by | 00000150 61 20 73 65 6d 69 2d 63 6f 6c 6f 6e 20 27 3b 27 |a semi-colon ';'| 00000160 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |. | 00000170 20 20 20 20 20 2d 20 63 6f 6d 6d 65 6e 74 73 2c | - comments,| 00000180 20 70 72 65 63 65 64 65 64 20 62 79 20 61 20 62 | preceded by a b| 00000190 61 63 6b 2d 73 6c 61 73 68 20 27 5c 27 0a 20 20 |ack-slash '\'. | 000001a0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000001b0 20 20 2d 20 74 68 65 20 63 6f 6d 62 69 6e 61 74 | - the combinat| 000001c0 69 6f 6e 20 6f 66 20 62 6f 74 68 20 63 6f 6d 6d |ion of both comm| 000001d0 61 6e 64 73 20 61 6e 64 20 63 6f 6d 6d 65 6e 74 |ands and comment| 000001e0 73 0a 0a 53 6f 6d 65 20 67 6f 6f 64 20 65 78 61 |s..Some good exa| 000001f0 6d 70 6c 65 73 20 6f 66 20 46 54 53 20 66 69 6c |mples of FTS fil| 00000200 65 73 20 63 61 6e 20 62 65 20 66 6f 75 6e 64 20 |es can be found | 00000210 69 6e 20 74 68 65 20 27 46 54 53 2d 46 69 6c 65 |in the 'FTS-File| 00000220 73 27 20 64 69 72 65 63 74 6f 72 79 2e 0a 0a 41 |s' directory...A| 00000230 20 64 65 73 63 72 69 70 74 69 6f 6e 20 6f 66 20 | description of | 00000240 65 61 63 68 20 69 6e 64 69 76 69 64 75 61 6c 20 |each individual | 00000250 63 6f 6d 6d 61 6e 64 20 66 6f 6c 6c 6f 77 73 20 |command follows | 00000260 75 6e 64 65 72 6e 65 61 74 68 3a 0a 0a 0a 43 6f |underneath:...Co| 00000270 6d 6d 61 6e 64 20 20 20 20 20 20 20 20 20 20 20 |mmand | 00000280 20 20 20 44 65 73 63 72 69 70 74 69 6f 6e 0a 2d | Description.-| 00000290 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| * 000002d0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 54 69 74 |------------.Tit| 000002e0 6c 65 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |le | 000002f0 20 20 53 65 74 73 20 74 68 65 20 74 69 74 6c 65 | Sets the title| 00000300 20 66 6f 72 20 74 68 65 20 63 75 72 72 65 6e 74 | for the current| 00000310 20 73 75 72 66 61 63 65 28 73 29 2e 20 54 68 69 | surface(s). Thi| 00000320 73 20 74 69 74 6c 65 20 69 73 0a 20 20 20 20 20 |s title is. | 00000330 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000340 75 73 65 64 20 66 6f 72 20 61 6c 6c 20 66 69 6c |used for all fil| 00000350 65 2d 68 61 6e 64 6c 69 6e 67 2e 20 41 20 73 74 |e-handling. A st| 00000360 72 69 6e 67 20 6f 66 20 6d 61 78 69 6d 75 6d 20 |ring of maximum | 00000370 65 69 67 68 74 0a 20 20 20 20 20 20 20 20 20 20 |eight. | 00000380 20 20 20 20 20 20 20 20 20 20 20 63 68 61 72 61 | chara| 00000390 63 74 65 72 73 20 69 73 20 67 69 76 65 6e 20 61 |cters is given a| 000003a0 73 20 74 68 65 20 73 6f 6c 65 20 70 61 72 61 6d |s the sole param| 000003b0 65 74 65 72 2e 0a 20 20 20 20 20 20 20 20 20 20 |eter.. | 000003c0 20 20 20 20 20 20 20 20 20 20 20 45 78 61 6d 70 | Examp| 000003d0 6c 65 3a 20 54 69 74 6c 65 20 53 6e 6f 77 79 0a |le: Title Snowy.| 000003e0 0a 46 72 61 6d 65 73 20 20 20 20 20 20 20 20 20 |.Frames | 000003f0 20 20 20 20 20 20 53 65 74 73 20 74 68 65 20 6d | Sets the m| 00000400 61 78 69 6d 75 6d 20 6e 75 6d 62 65 72 20 6f 66 |aximum number of| 00000410 20 27 66 72 61 6d 65 73 27 2e 20 54 68 65 20 70 | 'frames'. The p| 00000420 61 72 61 6d 65 74 65 72 20 69 73 20 61 6e 0a 20 |arameter is an. | 00000430 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000440 20 20 20 20 69 6e 74 65 67 65 72 2e 20 0a 20 20 | integer. . | 00000450 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000460 20 20 20 45 78 61 6d 70 6c 65 3a 20 46 72 61 6d | Example: Fram| 00000470 65 73 20 32 34 0a 0a 53 63 6f 70 65 20 20 20 20 |es 24..Scope | 00000480 20 20 20 20 20 20 20 20 20 20 20 20 53 65 74 73 | Sets| 00000490 20 74 68 65 20 72 61 6e 67 65 20 6f 66 20 66 72 | the range of fr| 000004a0 61 6d 65 73 20 74 6f 20 62 65 20 72 65 6e 64 65 |ames to be rende| 000004b0 72 65 64 2e 20 49 66 20 79 6f 75 20 68 61 76 65 |red. If you have| 000004c0 20 73 65 74 0a 20 20 20 20 20 20 20 20 20 20 20 | set. | 000004d0 20 20 20 20 20 20 20 20 20 20 74 68 65 20 6d 61 | the ma| 000004e0 78 69 6d 75 6d 20 6e 75 6d 62 65 72 20 6f 66 20 |ximum number of | 000004f0 66 72 61 6d 65 73 20 74 6f 2c 20 73 61 79 20 32 |frames to, say 2| 00000500 34 2c 20 69 74 20 69 73 20 70 6f 73 73 69 62 6c |4, it is possibl| 00000510 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |e. | 00000520 20 20 20 20 20 20 20 74 6f 20 73 65 74 20 74 68 | to set th| 00000530 65 20 72 61 6e 67 65 20 6f 66 20 66 72 61 6d 65 |e range of frame| 00000540 73 20 74 6f 20 62 65 20 72 65 6e 64 65 72 65 64 |s to be rendered| 00000550 20 74 6f 20 61 6e 79 0a 20 20 20 20 20 20 20 20 | to any. | 00000560 20 20 20 20 20 20 20 20 20 20 20 20 20 69 6e 74 | int| 00000570 65 72 76 61 6c 20 77 69 74 68 69 6e 20 31 2e 2e |erval within 1..| 00000580 32 34 2e 20 54 68 65 20 74 77 6f 20 70 61 72 61 |24. The two para| 00000590 6d 65 74 65 72 73 20 61 72 65 20 74 68 65 20 0a |meters are the .| 000005a0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000005b0 20 20 20 20 20 6d 69 6e 69 6d 75 6d 20 61 6e 64 | minimum and| 000005c0 20 6d 61 78 69 6d 75 6d 20 66 72 61 6d 65 20 6e | maximum frame n| 000005d0 75 6d 62 65 72 2e 0a 20 20 20 20 20 20 20 20 20 |umber.. | 000005e0 20 20 20 20 20 20 20 20 20 20 20 20 45 78 61 6d | Exam| 000005f0 70 6c 65 3a 20 53 63 6f 70 65 20 33 2c 31 38 0a |ple: Scope 3,18.| 00000600 0a 4d 61 6e 64 65 6c 62 72 6f 74 20 20 20 20 20 |.Mandelbrot | 00000610 20 20 20 20 20 20 54 65 6c 6c 73 20 74 68 65 20 | Tells the | 00000620 70 72 6f 67 72 61 6d 20 74 68 61 74 20 74 68 65 |program that the| 00000630 20 73 65 74 20 74 6f 20 62 65 20 75 73 65 64 20 | set to be used | 00000640 69 73 20 74 68 65 0a 20 20 20 20 20 20 20 20 20 |is the. | 00000650 20 20 20 20 20 20 20 20 20 20 20 20 4d 61 6e 64 | Mand| 00000660 65 6c 62 72 6f 74 20 53 65 74 2e 20 54 68 69 73 |elbrot Set. This| 00000670 20 63 6f 6d 6d 61 6e 64 20 74 61 6b 65 73 20 6e | command takes n| 00000680 6f 20 70 61 72 61 6d 65 74 65 72 73 2e 0a 0a 4a |o parameters...J| 00000690 75 6c 69 61 20 20 20 20 20 20 20 20 20 20 20 20 |ulia | 000006a0 20 20 20 20 54 65 6c 6c 73 20 74 68 65 20 70 72 | Tells the pr| 000006b0 6f 67 72 61 6d 20 74 68 61 74 20 74 68 65 20 73 |ogram that the s| 000006c0 65 74 20 74 6f 20 62 65 20 75 73 65 64 20 69 73 |et to be used is| 000006d0 20 61 20 4a 75 6c 69 61 0a 20 20 20 20 20 20 20 | a Julia. | 000006e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 53 65 | Se| 000006f0 74 2e 20 54 68 69 73 20 63 6f 6d 6d 61 6e 64 20 |t. This command | 00000700 74 61 6b 65 73 20 6e 6f 20 70 61 72 61 6d 65 74 |takes no paramet| 00000710 65 72 73 2e 0a 0a 52 65 73 6f 6c 75 74 69 6f 6e |ers...Resolution| 00000720 20 20 20 20 20 20 20 20 20 20 20 53 65 74 73 20 | Sets | 00000730 74 68 65 20 72 65 73 6f 6c 75 74 69 6f 6e 20 6f |the resolution o| 00000740 66 20 74 68 65 20 73 75 72 66 61 63 65 20 74 6f |f the surface to| 00000750 20 62 65 20 63 61 6c 63 75 6c 61 74 65 64 20 61 | be calculated a| 00000760 6e 64 2f 0a 20 20 20 20 20 20 20 20 20 20 20 20 |nd/. | 00000770 20 20 20 20 20 20 20 20 20 6f 72 20 72 65 6e 64 | or rend| 00000780 65 72 65 64 2e 20 54 68 65 20 75 6e 69 74 73 20 |ered. The units | 00000790 66 6f 72 20 74 68 69 73 20 72 65 73 6f 6c 75 74 |for this resolut| 000007a0 69 6f 6e 20 6d 61 79 20 62 65 20 0a 20 20 20 20 |ion may be . | 000007b0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000007c0 20 72 65 67 61 72 64 65 64 20 61 73 20 70 69 78 | regarded as pix| 000007d0 65 6c 73 2e 20 54 68 65 20 74 77 6f 20 70 61 72 |els. The two par| 000007e0 61 6d 65 74 65 72 73 20 61 72 65 20 74 68 65 20 |ameters are the | 000007f0 78 20 61 6e 64 20 79 20 0a 20 20 20 20 20 20 20 |x and y . | 00000800 20 20 20 20 20 20 20 20 20 20 20 20 20 20 72 65 | re| 00000810 73 6f 6c 75 74 69 6f 6e 20 6f 66 20 74 68 65 20 |solution of the | 00000820 73 75 72 66 61 63 65 2e 0a 20 20 20 20 20 20 20 |surface.. | 00000830 20 20 20 20 20 20 20 20 20 20 20 20 20 20 45 78 | Ex| 00000840 61 6d 70 6c 65 3a 20 52 65 73 6f 6c 75 74 69 6f |ample: Resolutio| 00000850 6e 20 33 30 30 2c 33 30 30 0a 0a 52 61 6e 67 65 |n 300,300..Range| 00000860 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000870 53 65 74 73 20 74 68 65 20 72 61 6e 67 65 20 69 |Sets the range i| 00000880 6e 20 74 68 65 20 63 6f 6d 70 6c 65 78 20 70 6c |n the complex pl| 00000890 61 6e 65 20 66 6f 72 20 74 68 65 20 70 61 72 74 |ane for the part| 000008a0 20 6f 66 20 74 68 65 0a 20 20 20 20 20 20 20 20 | of the. | 000008b0 20 20 20 20 20 20 20 20 20 20 20 20 20 73 65 74 | set| 000008c0 20 74 68 61 74 20 69 73 20 74 6f 20 62 65 20 63 | that is to be c| 000008d0 61 6c 63 75 6c 61 74 65 64 20 61 6e 64 2f 6f 72 |alculated and/or| 000008e0 20 72 65 6e 64 65 72 65 64 2e 20 54 68 65 20 66 | rendered. The f| 000008f0 6f 75 72 0a 20 20 20 20 20 20 20 20 20 20 20 20 |our. | 00000900 20 20 20 20 20 20 20 20 20 70 61 72 61 6d 65 74 | paramet| 00000910 65 72 73 20 61 72 65 20 6d 69 6e 69 6d 75 6d 20 |ers are minimum | 00000920 78 2c 20 6d 61 78 69 6d 75 6d 20 78 20 28 72 65 |x, maximum x (re| 00000930 61 6c 20 61 78 69 73 29 2c 20 6d 69 6e 69 6d 75 |al axis), minimu| 00000940 6d 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |m. | 00000950 20 20 20 20 20 20 20 79 2c 20 6d 61 78 69 6d 75 | y, maximu| 00000960 6d 20 79 20 28 69 6d 61 67 69 6e 61 72 79 20 61 |m y (imaginary a| 00000970 78 69 73 29 2e 20 54 68 65 73 65 20 76 61 6c 75 |xis). These valu| 00000980 65 73 20 63 61 6e 20 62 65 73 74 20 62 65 0a 20 |es can best be. | 00000990 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000009a0 20 20 20 20 6f 62 74 61 69 6e 65 64 20 66 72 6f | obtained fro| 000009b0 6d 20 61 20 6e 6f 72 6d 61 6c 20 4d 61 6e 64 65 |m a normal Mande| 000009c0 6c 62 72 6f 74 20 70 6c 6f 74 74 69 6e 67 20 70 |lbrot plotting p| 000009d0 72 6f 67 72 61 6d 21 0a 20 20 20 20 20 20 20 20 |rogram!. | 000009e0 20 20 20 20 20 20 20 20 20 20 20 20 20 45 78 61 | Exa| 000009f0 6d 70 6c 65 3a 20 52 61 6e 67 65 20 2d 31 2e 35 |mple: Range -1.5| 00000a00 2c 31 2e 35 2c 2d 31 2e 35 2c 31 2e 35 0a 0a 43 |,1.5,-1.5,1.5..C| 00000a10 76 61 6c 20 20 20 20 20 20 20 20 20 20 20 20 20 |val | 00000a20 20 20 20 20 53 65 74 73 20 74 68 65 20 72 65 61 | Sets the rea| 00000a30 6c 20 61 6e 64 20 69 6d 61 67 69 6e 61 72 79 20 |l and imaginary | 00000a40 70 61 72 74 20 6f 66 20 74 68 65 20 70 6f 69 6e |part of the poin| 00000a50 74 20 74 6f 20 0a 20 20 20 20 20 20 20 20 20 20 |t to . | 00000a60 20 20 20 20 20 20 20 20 20 20 20 63 61 6c 63 75 | calcu| 00000a70 6c 61 74 65 20 61 6e 64 2f 6f 72 20 72 65 6e 64 |late and/or rend| 00000a80 65 72 20 74 68 65 20 4a 75 6c 69 61 20 53 65 74 |er the Julia Set| 00000a90 20 6f 66 2e 20 54 68 65 20 74 77 6f 20 0a 20 20 | of. The two . | 00000aa0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000ab0 20 20 20 70 61 72 61 6d 65 74 65 72 73 20 61 72 | parameters ar| 00000ac0 65 20 74 68 65 20 72 65 61 6c 20 61 6e 64 20 69 |e the real and i| 00000ad0 6d 61 67 69 6e 61 72 79 20 70 61 72 74 20 6f 66 |maginary part of| 00000ae0 20 74 68 65 20 70 6f 69 6e 74 2e 0a 20 20 20 20 | the point.. | 00000af0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000b00 20 45 78 61 6d 70 6c 65 3a 20 43 76 61 6c 20 30 | Example: Cval 0| 00000b10 2e 33 32 2c 30 2e 30 34 33 0a 0a 53 6d 6f 6f 74 |.32,0.043..Smoot| 00000b20 68 6e 65 73 73 20 20 20 20 20 20 20 20 20 20 20 |hness | 00000b30 53 65 74 73 20 74 68 65 20 73 6d 6f 6f 74 68 6e |Sets the smoothn| 00000b40 65 73 73 20 6f 66 20 74 68 65 20 73 75 72 66 61 |ess of the surfa| 00000b50 63 65 2e 20 54 68 65 20 68 69 67 68 65 72 20 74 |ce. The higher t| 00000b60 68 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 |he. | 00000b70 20 20 20 20 20 20 20 20 73 6d 6f 6f 74 68 6e 65 | smoothne| 00000b80 73 73 2d 76 61 6c 75 65 2c 20 74 68 65 20 73 6d |ss-value, the sm| 00000b90 6f 6f 74 68 65 72 20 74 68 65 20 73 75 72 66 61 |oother the surfa| 00000ba0 63 65 2c 20 61 6e 64 20 74 68 65 20 6d 6f 72 65 |ce, and the more| 00000bb0 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |. | 00000bc0 20 20 20 20 20 20 63 61 6c 63 75 6c 61 74 69 6f | calculatio| 00000bd0 6e 73 20 77 69 6c 6c 20 62 65 20 70 65 72 66 6f |ns will be perfo| 00000be0 72 6d 65 64 20 74 6f 20 6f 62 74 61 69 6e 20 74 |rmed to obtain t| 00000bf0 68 65 20 70 6f 74 65 6e 74 69 61 6c 20 0a 20 20 |he potential . | 00000c00 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000c10 20 20 20 6f 66 20 61 20 70 6f 69 6e 74 20 6f 6e | of a point on| 00000c20 20 74 68 65 20 73 75 72 66 61 63 65 21 20 54 68 | the surface! Th| 00000c30 65 20 73 6f 6c 65 20 70 61 72 61 6d 65 74 65 72 |e sole parameter| 00000c40 20 69 73 20 61 6e 0a 20 20 20 20 20 20 20 20 20 | is an. | 00000c50 20 20 20 20 20 20 20 20 20 20 20 20 69 6e 74 65 | inte| 00000c60 67 65 72 2c 20 77 68 69 63 68 20 72 65 61 6c 6c |ger, which reall| 00000c70 79 20 73 68 6f 75 6c 64 20 62 65 20 61 74 20 6c |y should be at l| 00000c80 65 61 73 74 20 61 62 6f 75 74 20 31 30 30 21 0a |east about 100!.| 00000c90 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000ca0 20 20 20 20 20 45 78 61 6d 70 6c 65 3a 20 53 6d | Example: Sm| 00000cb0 6f 6f 74 68 6e 65 73 73 20 31 32 30 0a 0a 44 65 |oothness 120..De| 00000cc0 70 74 68 20 20 20 20 20 20 20 20 20 20 20 20 20 |pth | 00000cd0 20 20 20 53 65 74 73 20 74 68 65 20 64 65 70 74 | Sets the dept| 00000ce0 68 20 6f 66 20 74 68 65 20 69 74 65 72 61 74 69 |h of the iterati| 00000cf0 6f 6e 73 20 69 6e 20 74 68 65 20 63 61 6c 63 75 |ons in the calcu| 00000d00 6c 61 74 69 6f 6e 20 6f 66 20 0a 20 20 20 20 20 |lation of . | 00000d10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000d20 74 68 65 20 70 6f 74 65 6e 74 69 61 6c 20 6f 66 |the potential of| 00000d30 20 61 20 70 6f 69 6e 74 2e 20 54 68 65 20 68 69 | a point. The hi| 00000d40 67 68 65 72 20 74 68 65 20 76 61 6c 75 65 2c 20 |gher the value, | 00000d50 74 68 65 20 6d 6f 72 65 0a 20 20 20 20 20 20 20 |the more. | 00000d60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 70 72 | pr| 00000d70 65 63 69 73 65 20 74 68 65 20 73 65 74 20 77 69 |ecise the set wi| 00000d80 6c 6c 20 62 65 20 63 61 6c 63 75 6c 61 74 65 64 |ll be calculated| 00000d90 2c 20 61 6e 64 20 61 67 61 69 6e 2c 20 74 68 65 |, and again, the| 00000da0 20 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | . | 00000db0 20 20 20 20 20 20 20 6c 6f 6e 67 65 72 20 69 74 | longer it| 00000dc0 20 74 61 6b 65 73 20 74 6f 20 63 61 6c 63 75 6c | takes to calcul| 00000dd0 61 74 65 20 61 20 70 6f 69 6e 74 2d 70 6f 74 65 |ate a point-pote| 00000de0 6e 74 69 61 6c 2e 20 54 68 65 20 0a 20 20 20 20 |ntial. The . | 00000df0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000e00 20 70 61 72 61 6d 65 74 65 72 20 69 73 20 61 6e | parameter is an| 00000e10 20 69 6e 74 65 67 65 72 20 69 6e 20 74 68 65 20 | integer in the | 00000e20 72 61 6e 67 65 20 31 2e 2e 31 32 37 21 21 21 0a |range 1..127!!!.| 00000e30 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000e40 20 20 20 20 20 45 78 61 6d 70 6c 65 3a 20 44 65 | Example: De| 00000e50 70 74 68 20 31 30 30 0a 0a 4d 6f 75 6e 74 61 69 |pth 100..Mountai| 00000e60 6e 73 20 20 20 20 20 20 20 20 20 20 20 20 54 65 |ns Te| 00000e70 6c 6c 73 20 74 68 65 20 70 72 6f 67 72 61 6d 20 |lls the program | 00000e80 74 6f 20 72 65 6e 64 65 72 20 74 68 65 20 73 75 |to render the su| 00000e90 72 66 61 63 65 20 61 73 20 61 20 6d 6f 75 6e 74 |rface as a mount| 00000ea0 61 69 6e 2e 0a 20 20 20 20 20 20 20 20 20 20 20 |ain.. | 00000eb0 20 20 20 20 20 20 20 20 20 20 54 68 69 73 20 63 | This c| 00000ec0 6f 6d 6d 61 6e 64 20 74 61 6b 65 73 20 6e 6f 20 |ommand takes no | 00000ed0 70 61 72 61 6d 65 74 65 72 73 2e 0a 0a 56 61 6c |parameters...Val| 00000ee0 6c 65 79 73 20 20 20 20 20 20 20 20 20 20 20 20 |leys | 00000ef0 20 20 54 65 6c 6c 73 20 74 68 65 20 70 72 6f 67 | Tells the prog| 00000f00 72 61 6d 20 74 6f 20 72 65 6e 64 65 72 20 74 68 |ram to render th| 00000f10 65 20 73 75 72 66 61 63 65 20 61 73 20 61 20 76 |e surface as a v| 00000f20 61 6c 6c 65 79 2e 0a 20 20 20 20 20 20 20 20 20 |alley.. | 00000f30 20 20 20 20 20 20 20 20 20 20 20 20 54 68 69 73 | This| 00000f40 20 63 6f 6d 6d 61 6e 64 20 74 61 6b 65 73 20 6e | command takes n| 00000f50 6f 20 70 61 72 61 6d 65 74 65 72 73 2e 0a 0a 4c |o parameters...L| 00000f60 69 67 68 74 20 20 20 20 20 20 20 20 20 20 20 20 |ight | 00000f70 20 20 20 20 53 65 74 73 20 74 68 65 20 64 69 72 | Sets the dir| 00000f80 65 63 74 69 6f 6e 20 6f 66 20 74 68 65 20 6c 69 |ection of the li| 00000f90 67 68 74 2d 76 65 63 74 6f 72 2e 20 54 68 69 73 |ght-vector. This| 00000fa0 20 76 65 63 74 6f 72 0a 20 20 20 20 20 20 20 20 | vector. | 00000fb0 20 20 20 20 20 20 20 20 20 20 20 20 20 6e 65 65 | nee| 00000fc0 64 20 6e 6f 74 20 62 65 20 6e 6f 72 6d 61 6c 69 |d not be normali| 00000fd0 73 65 64 2e 20 4e 6f 74 65 20 74 68 61 74 20 74 |sed. Note that t| 00000fe0 68 69 73 20 76 65 63 74 6f 72 20 69 73 20 74 68 |his vector is th| 00000ff0 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |e. | 00001000 20 20 20 20 20 20 20 64 69 72 65 63 74 69 6f 6e | direction| 00001010 20 6f 66 20 74 68 65 20 6c 69 67 68 74 2d 72 61 | of the light-ra| 00001020 79 73 2c 20 69 65 2e 20 69 74 20 70 6f 69 6e 74 |ys, ie. it point| 00001030 73 20 61 77 61 79 20 66 72 6f 6d 20 74 68 65 0a |s away from the.| 00001040 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00001050 20 20 20 20 20 6c 69 67 68 74 20 73 6f 75 72 63 | light sourc| 00001060 65 21 20 54 68 65 20 74 68 72 65 65 20 70 61 72 |e! The three par| 00001070 61 6d 65 74 65 72 73 20 61 72 65 20 74 68 65 20 |ameters are the | 00001080 78 2c 20 79 2c 20 61 6e 64 20 7a 0a 20 20 20 20 |x, y, and z. | 00001090 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000010a0 20 63 6f 6d 70 6f 6e 65 6e 74 73 20 6f 66 20 74 | components of t| 000010b0 68 65 20 76 65 63 74 6f 72 2e 20 28 7a 20 61 6c |he vector. (z al| 000010c0 77 61 79 73 20 73 68 6f 75 6c 64 20 62 65 20 6e |ways should be n| 000010d0 65 67 61 74 69 76 65 21 29 0a 20 20 20 20 20 20 |egative!). | 000010e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 45 | E| 000010f0 78 61 6d 70 6c 65 3a 20 4c 69 67 68 74 20 30 2e |xample: Light 0.| 00001100 35 2c 31 2c 2d 32 20 20 20 20 20 20 20 20 0a 0a |5,1,-2 ..| 00001110 42 72 69 67 68 74 6e 65 73 73 20 20 20 20 20 20 |Brightness | 00001120 20 20 20 20 20 53 65 74 73 20 74 68 65 20 62 72 | Sets the br| 00001130 69 67 68 74 6e 65 73 73 20 6f 66 20 74 68 65 20 |ightness of the | 00001140 6c 69 67 68 74 2d 73 6f 75 72 63 65 2e 20 54 68 |light-source. Th| 00001150 65 20 68 69 67 68 65 72 20 74 68 65 0a 20 20 20 |e higher the. | 00001160 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00001170 20 20 76 61 6c 75 65 2c 20 74 68 65 20 62 72 69 | value, the bri| 00001180 67 68 74 65 72 20 74 68 65 20 6c 69 67 68 74 2e |ghter the light.| 00001190 20 54 68 65 20 73 6f 6c 65 20 70 61 72 61 6d 65 | The sole parame| 000011a0 74 65 72 20 69 73 20 61 6e 0a 20 20 20 20 20 20 |ter is an. | 000011b0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 69 | i| 000011c0 6e 74 65 67 65 72 2e 0a 20 20 20 20 20 20 20 20 |nteger.. | 000011d0 20 20 20 20 20 20 20 20 20 20 20 20 20 45 78 61 | Exa| 000011e0 6d 70 6c 65 3a 20 42 72 69 67 68 74 6e 65 73 73 |mple: Brightness| 000011f0 20 37 38 0a 0a 53 74 65 65 70 6e 65 73 73 20 20 | 78..Steepness | 00001200 20 20 20 20 20 20 20 20 20 20 53 65 74 73 20 74 | Sets t| 00001210 68 65 20 73 74 65 65 70 6e 65 73 73 20 6f 66 20 |he steepness of | 00001220 74 68 65 20 6d 6f 75 6e 74 61 69 6e 2f 76 61 6c |the mountain/val| 00001230 6c 65 79 20 73 6c 6f 70 65 73 2e 20 54 68 65 0a |ley slopes. The.| 00001240 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00001250 20 20 20 20 20 68 69 67 68 65 72 20 74 68 65 20 | higher the | 00001260 76 61 6c 75 65 2c 20 74 68 65 20 73 74 65 65 70 |value, the steep| 00001270 65 72 20 74 68 65 20 73 6c 6f 70 65 73 2e 20 4e |er the slopes. N| 00001280 6f 74 65 20 74 68 61 74 20 74 68 65 0a 20 20 20 |ote that the. | 00001290 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000012a0 20 20 6d 61 67 6e 69 74 75 64 65 20 6f 66 20 74 | magnitude of t| 000012b0 68 69 73 20 76 61 6c 75 65 20 69 73 20 64 69 73 |his value is dis| 000012c0 70 72 6f 70 6f 72 74 69 6f 6e 61 6c 20 77 69 74 |proportional wit| 000012d0 68 20 73 69 7a 65 20 6f 66 0a 20 20 20 20 20 20 |h size of. | 000012e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 74 | t| 000012f0 68 65 20 72 65 67 69 6f 6e 20 69 6e 64 69 63 61 |he region indica| 00001300 74 65 64 20 77 69 74 68 20 74 68 65 20 72 61 6e |ted with the ran| 00001310 67 65 20 63 6f 6d 6d 61 6e 64 2e 20 54 68 65 20 |ge command. The | 00001320 73 6f 6c 65 0a 20 20 20 20 20 20 20 20 20 20 20 |sole. | 00001330 20 20 20 20 20 20 20 20 20 20 70 61 72 61 6d 65 | parame| 00001340 74 65 72 20 69 73 20 61 6e 20 69 6e 74 65 67 65 |ter is an intege| 00001350 72 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 |r.. | 00001360 20 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 3a | Example:| 00001370 20 53 74 65 65 70 6e 65 73 73 20 32 34 30 0a 0a | Steepness 240..| 00001380 44 69 74 68 65 72 69 6e 67 20 20 20 20 20 20 20 |Dithering | 00001390 20 20 20 20 20 53 65 74 73 20 74 68 65 20 63 6f | Sets the co| 000013a0 6c 6f 72 2d 64 69 74 68 65 72 69 6e 67 20 66 61 |lor-dithering fa| 000013b0 63 74 6f 72 2e 20 42 65 63 61 75 73 65 20 74 68 |ctor. Because th| 000013c0 65 20 70 72 6f 67 72 61 6d 0a 20 20 20 20 20 20 |e program. | 000013d0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 6f | o| 000013e0 6e 6c 79 20 75 73 65 73 20 31 36 20 63 6f 6c 6f |nly uses 16 colo| 000013f0 72 73 20 74 6f 20 72 65 6e 64 65 72 20 61 6e 20 |rs to render an | 00001400 69 6d 61 67 65 20 28 64 75 65 20 74 6f 20 74 68 |image (due to th| 00001410 65 20 34 62 69 74 0a 20 20 20 20 20 20 20 20 20 |e 4bit. | 00001420 20 20 20 20 20 20 20 20 20 20 20 20 6e 61 74 75 | natu| 00001430 72 65 20 6f 66 20 6d 6f 64 65 20 31 32 29 2c 20 |re of mode 12), | 00001440 61 62 72 75 70 74 20 63 6f 6c 6f 72 20 63 68 61 |abrupt color cha| 00001450 6e 67 65 73 20 6f 6e 20 74 68 65 20 73 75 72 66 |nges on the surf| 00001460 61 63 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 |ace. | 00001470 20 20 20 20 20 20 20 20 20 6d 61 79 20 67 69 76 | may giv| 00001480 65 20 61 20 6e 6f 6e 2d 72 65 61 6c 69 73 74 69 |e a non-realisti| 00001490 63 20 66 65 65 6c 20 74 6f 20 74 68 65 20 69 6d |c feel to the im| 000014a0 61 67 65 2e 20 54 68 65 72 65 66 6f 72 65 2c 0a |age. Therefore,.| 000014b0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000014c0 20 20 20 20 20 61 20 73 69 6d 70 6c 65 20 74 65 | a simple te| 000014d0 63 68 6e 69 71 75 65 2c 20 63 61 6c 6c 65 64 20 |chnique, called | 000014e0 72 61 6e 64 6f 6d 20 64 69 74 68 65 72 69 6e 67 |random dithering| 000014f0 2c 20 69 73 20 75 73 65 64 20 74 6f 0a 20 20 20 |, is used to. | 00001500 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00001510 20 20 70 72 6f 64 75 63 65 20 69 6e 74 65 72 6d | produce interm| 00001520 65 64 69 61 74 65 20 27 70 73 65 75 64 6f 2d 63 |ediate 'pseudo-c| 00001530 6f 6c 6f 72 73 27 2c 20 77 68 69 63 68 20 6d 61 |olors', which ma| 00001540 6b 65 20 74 68 65 0a 20 20 20 20 20 20 20 20 20 |ke the. | 00001550 20 20 20 20 20 20 20 20 20 20 20 20 63 6f 6c 6f | colo| 00001560 72 20 63 68 61 6e 67 65 73 20 73 65 65 6d 20 71 |r changes seem q| 00001570 75 69 74 65 20 63 6f 6e 74 69 6e 75 6f 75 73 2e |uite continuous.| 00001580 20 41 20 76 61 6c 75 65 20 6f 66 20 31 20 6d 65 | A value of 1 me| 00001590 61 6e 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 |ans. | 000015a0 20 20 20 20 20 20 20 20 20 6e 6f 20 63 6f 6c 6f | no colo| 000015b0 72 20 64 69 74 68 65 72 69 6e 67 2e 20 54 68 65 |r dithering. The| 000015c0 20 73 6f 6c 65 20 70 61 72 61 6d 65 74 65 72 20 | sole parameter | 000015d0 69 73 20 61 6e 20 69 6e 74 65 67 65 72 2e 0a 20 |is an integer.. | 000015e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000015f0 20 20 20 20 45 78 61 6d 70 6c 65 3a 20 44 69 74 | Example: Dit| 00001600 68 65 72 69 6e 67 20 31 36 0a 0a 53 68 61 64 6f |hering 16..Shado| 00001610 77 73 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |ws | 00001620 54 65 6c 6c 73 20 74 68 65 20 70 72 6f 67 72 61 |Tells the progra| 00001630 6d 20 77 68 65 74 68 65 72 20 74 6f 20 63 61 6c |m whether to cal| 00001640 63 75 6c 61 74 65 20 73 68 61 64 6f 77 73 20 6f |culate shadows o| 00001650 72 20 6e 6f 74 2e 0a 20 20 20 20 20 20 20 20 20 |r not.. | 00001660 20 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 | The | 00001670 63 61 6c 63 75 6c 61 74 69 6f 6e 20 6f 66 20 73 |calculation of s| 00001680 68 61 64 6f 77 73 20 73 6c 6f 77 73 20 64 6f 77 |hadows slows dow| 00001690 6e 20 74 68 65 20 72 65 6e 64 65 72 69 6e 67 0a |n the rendering.| 000016a0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000016b0 20 20 20 20 20 71 75 69 74 65 20 64 72 61 73 74 | quite drast| 000016c0 69 63 61 6c 6c 79 2e 20 54 68 65 20 70 61 72 61 |ically. The para| 000016d0 6d 65 74 65 72 20 69 73 20 61 20 73 74 72 69 6e |meter is a strin| 000016e0 67 20 6f 66 20 74 68 65 20 66 6f 72 6d 0a 20 20 |g of the form. | 000016f0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00001700 20 20 20 27 4f 6e 27 20 6f 72 20 27 4f 66 66 27 | 'On' or 'Off'| 00001710 2e 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |.. | 00001720 20 20 20 20 20 20 20 45 78 61 6d 70 6c 65 3a 20 | Example: | 00001730 53 68 61 64 6f 77 73 20 4f 6e 0a 0a 49 6e 74 65 |Shadows On..Inte| 00001740 72 70 6f 6c 61 74 69 6f 6e 20 20 20 20 20 20 20 |rpolation | 00001750 20 54 65 6c 6c 73 20 74 68 65 20 70 72 6f 67 72 | Tells the progr| 00001760 61 6d 20 77 68 65 74 68 65 72 20 74 6f 20 69 6e |am whether to in| 00001770 74 65 72 70 6f 6c 61 74 65 20 76 61 6c 75 65 73 |terpolate values| 00001780 20 69 6e 20 74 68 65 0a 20 20 20 20 20 20 20 20 | in the. | 00001790 20 20 20 20 20 20 20 20 20 20 20 20 20 68 6f 72 | hor| 000017a0 69 7a 6f 6e 74 61 6c 20 64 69 72 65 63 74 69 6f |izontal directio| 000017b0 6e 2e 20 49 6e 74 65 72 70 6f 6c 61 74 69 6e 67 |n. 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'fo| 000036e0 72 20 63 6e 74 3d 2d 33 20 74 6f 20 6d 61 78 20 |r cnt=-3 to max | 000036f0 62 79 20 32 27 20 6f 72 20 27 66 6f 72 20 73 69 |by 2' or 'for si| 00003700 7a 65 3d 32 20 74 6f 20 31 20 62 79 20 2d 30 2e |ze=2 to 1 by -0.| 00003710 31 27 2c 0a 20 20 20 61 6e 64 20 27 76 61 72 69 |1',. and 'vari| 00003720 61 62 6c 65 27 20 74 68 65 20 6e 61 6d 65 20 6f |able' the name o| 00003730 66 20 61 20 75 73 65 72 2d 76 61 72 69 61 62 6c |f a user-variabl| 00003740 65 2e 0a 20 20 20 45 61 63 68 20 6f 70 65 6e 69 |e.. Each openi| 00003750 6e 67 20 27 66 6f 72 27 20 6d 75 73 74 20 68 61 |ng 'for' must ha| 00003760 76 65 20 61 20 63 6c 6f 73 69 6e 67 20 27 65 6e |ve a closing 'en| 00003770 64 66 6f 72 27 2e 0a 20 20 20 54 68 65 20 27 66 |dfor'.. 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'.routi| 000038a0 6e 65 31 27 2e 0a 53 75 63 68 20 73 75 62 72 6f |ne1'..Such subro| 000038b0 75 74 69 6e 65 73 20 61 72 65 20 63 61 6c 6c 65 |utines are calle| 000038c0 64 20 69 6e 20 74 68 65 20 66 6f 6c 6c 6f 77 69 |d in the followi| 000038d0 6e 67 20 77 61 79 3a 0a 0a 20 20 20 20 20 20 63 |ng way:.. c| 000038e0 6f 6d 6d 61 6e 64 73 20 20 20 20 20 20 20 20 20 |ommands | 000038f0 20 20 20 20 5c 0a 20 20 20 20 20 20 20 20 20 2e | \. .| 00003900 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00003910 20 20 5c 0a 20 20 20 20 20 20 20 20 20 2e 20 20 | \. . | 00003920 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00003930 20 5c 0a 20 20 20 20 20 20 63 61 6c 6c 20 6c 61 | \. call la| 00003940 62 65 6c 6e 61 6d 65 20 20 20 20 20 20 20 20 20 |belname | 00003950 20 3e 20 6d 61 69 6e 20 70 72 6f 67 72 61 6d 0a | > main program.| 00003960 20 20 20 20 20 20 20 20 20 2e 20 20 20 20 20 20 | . | 00003970 20 20 20 20 20 20 20 20 20 20 20 20 20 2f 0a 20 | /. | 00003980 20 20 20 20 20 20 20 20 2e 20 20 20 20 20 20 20 | . | 00003990 20 20 20 20 20 20 20 20 20 20 20 2f 0a 20 20 20 | /. | 000039a0 20 20 20 73 74 6f 70 20 20 20 20 20 20 20 20 20 | stop | 000039b0 20 20 20 20 20 20 20 20 2f 0a 0a 20 20 20 20 20 | /.. | 000039c0 20 2e 6c 61 62 65 6c 6e 61 6d 65 20 20 20 20 20 | .labelname | 000039d0 20 20 20 20 20 20 20 5c 0a 20 20 20 20 20 20 20 | \. | 000039e0 63 6f 6d 6d 61 6e 64 73 20 20 20 20 20 20 20 20 |commands | 000039f0 20 20 20 20 20 20 5c 0a 20 20 20 20 20 20 20 20 | \. | 00003a00 20 20 2e 20 20 20 20 20 20 20 20 20 20 20 20 20 | . | 00003a10 20 20 20 20 20 20 3e 20 73 75 62 72 6f 75 74 69 | > subrouti| 00003a20 6e 65 20 27 6c 61 62 65 6c 6e 61 6d 65 27 0a 20 |ne 'labelname'. | 00003a30 20 20 20 20 20 20 20 20 20 2e 20 20 20 20 20 20 | . | 00003a40 20 20 20 20 20 20 20 20 20 20 20 20 2f 0a 20 20 | /. | 00003a50 20 20 20 20 20 72 65 74 75 72 6e 20 20 20 20 20 | return | 00003a60 20 20 20 20 20 20 20 20 20 20 2f 0a 20 20 20 20 | /. | 00003a70 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00003a80 20 20 20 20 20 20 20 20 20 20 20 20 0a 41 73 20 | .As | 00003a90 79 6f 75 20 63 61 6e 20 73 65 65 2c 20 65 78 65 |you can see, exe| 00003aa0 63 75 74 69 6f 6e 20 6f 66 20 61 20 73 75 62 72 |cution of a subr| 00003ab0 6f 75 74 69 6e 65 20 69 73 20 73 74 61 72 74 65 |outine is starte| 00003ac0 64 20 77 69 74 68 20 61 20 27 63 61 6c 6c 27 20 |d with a 'call' | 00003ad0 63 6f 6d 6d 61 6e 64 2c 0a 61 6e 64 20 65 6e 64 |command,.and end| 00003ae0 73 20 77 69 74 68 20 61 20 27 72 65 74 75 72 6e |s with a 'return| 00003af0 27 20 63 6f 6d 6d 61 6e 64 2e 20 54 68 65 72 65 |' command. There| 00003b00 66 6f 72 65 2c 20 65 61 63 68 20 27 63 61 6c 6c |fore, each 'call| 00003b10 27 20 4d 55 53 54 20 68 61 76 65 20 61 0a 27 72 |' MUST have a.'r| 00003b20 65 74 75 72 6e 27 21 21 21 0a 54 68 65 20 73 75 |eturn'!!!.The su| 00003b30 62 72 6f 75 74 69 6e 65 2d 63 61 6c 6c 73 20 69 |broutine-calls i| 00003b40 65 2e 20 27 63 61 6c 6c 20 2e 2e 20 72 65 74 75 |e. 'call .. retu| 00003b50 72 6e 27 20 6d 61 79 20 62 65 20 6e 65 73 74 65 |rn' may be neste| 00003b60 64 20 75 70 20 74 6f 20 33 32 20 6c 65 76 65 6c |d up to 32 level| 00003b70 73 0a 64 65 65 70 2e 20 28 54 68 61 74 20 69 6e |s.deep. (That in| 00003b80 63 6c 75 64 65 73 20 72 65 63 75 72 73 69 6f 6e |cludes recursion| 00003b90 21 29 0a 0a 0a 57 72 69 74 69 6e 67 20 70 72 6f |!)...Writing pro| 00003ba0 67 72 61 6d 73 0a 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |grams.----------| 00003bb0 2d 2d 2d 2d 2d 2d 0a 0a 59 6f 75 20 77 69 6c 6c |------..You will| 00003bc0 20 63 65 72 74 61 69 6e 6c 79 20 68 61 76 65 20 | certainly have | 00003bd0 6e 6f 74 69 63 65 64 20 66 72 6f 6d 20 74 68 65 |noticed from the| 00003be0 20 6c 61 73 74 20 74 68 72 65 65 20 70 61 72 61 | last three para| 00003bf0 67 72 61 70 68 73 20 74 68 61 74 20 69 74 20 69 |graphs that it i| 00003c00 73 0a 70 6f 73 73 69 62 6c 65 20 74 6f 20 62 75 |s.possible to bu| 00003c10 69 6c 64 20 73 6d 61 6c 6c 20 70 72 6f 67 72 61 |ild small progra| 00003c20 6d 73 20 75 73 69 6e 67 20 74 68 65 20 63 6f 6e |ms using the con| 00003c30 74 72 6f 6c 20 63 6f 6e 73 74 72 75 63 74 73 20 |trol constructs | 00003c40 61 6e 64 20 76 61 72 69 61 62 6c 65 73 0a 70 72 |and variables.pr| 00003c50 6f 76 69 64 65 64 20 62 79 20 46 72 61 63 54 72 |ovided by FracTr| 00003c60 61 63 65 2e 20 54 68 65 73 65 20 70 72 6f 67 72 |ace. These progr| 00003c70 61 6d 73 20 64 6f 6e 27 74 20 68 61 76 65 20 74 |ams don't have t| 00003c80 6f 20 64 65 66 69 6e 65 20 61 20 66 72 61 63 74 |o define a fract| 00003c90 61 6c 20 73 75 72 66 61 63 65 0a 28 74 68 65 79 |al surface.(they| 00003ca0 20 6d 61 79 20 64 6f 21 29 2c 20 74 68 65 79 20 | may do!), they | 00003cb0 63 61 6e 20 61 6c 73 6f 20 62 65 20 75 73 65 64 |can also be used| 00003cc0 20 74 6f 20 73 6f 6c 76 65 20 77 68 61 74 65 76 | to solve whatev| 00003cd0 65 72 20 2d 20 73 6d 61 6c 6c 20 2d 20 70 72 6f |er - small - pro| 00003ce0 62 6c 65 6d 21 0a 54 68 65 20 46 54 53 20 66 69 |blem!.The FTS fi| 00003cf0 6c 65 73 20 27 46 61 63 74 6f 72 69 61 6c 27 2c |les 'Factorial',| 00003d00 20 27 46 69 62 6f 6e 61 63 63 69 27 2c 20 27 53 | 'Fibonacci', 'S| 00003d10 75 6d 35 30 27 20 61 6e 64 20 27 4d 61 6e 64 65 |um50' and 'Mande| 00003d20 6c 50 6f 74 27 20 61 72 65 20 73 6f 6d 65 0a 65 |lPot' are some.e| 00003d30 78 61 6d 70 6c 65 73 20 6f 66 20 73 75 63 68 20 |xamples of such | 00003d40 73 6d 61 6c 6c 20 70 72 6f 67 72 61 6d 73 2e 0a |small programs..| 00003d50 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |. | 00003d60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00003d80 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 43 | C| 00003d90 61 72 6c 20 44 65 63 6c 65 72 63 6b 2e 0a |arl Declerck..| 00003d9e
.