vanroy@ji.Berkeley.EDU (Peter Van Roy) (07/09/88)
%!
% Postscript Fractal Drawing Program
% Copyright (C) 1988 by Peter Van Roy. All rights reserved.
% This program may be copied and used for non-commercial purposes
% provided this copyright notice is included unchanged.
% The examples in this file were first created interactively
% with the Macintosh program FractaSketch.
% Have fun with this little program!
% Please let me know if you have comments or suggestions.
% Peter Van Roy
% 508-10 Evans Hall
% Computer Science Division
% University of California
% Berkeley, CA 94720
% -----------------------------------------------------------------------------
% Some example fractals:
% Remove comments from the fractal you wish to draw.
% Koch snowflake:
/numpt 5 def
/slst [ 0 0.33333 0.33333 0.33333 0.33333 ] def
/relalst [ 0 60 -120 60 0 ] def
/backflags [ false false false false false ] def
/botflags [ false false false false false ] def
/invflags [ false false false false false ] def
/leftflags [ true true true true true ] def
/drawlevel 6 def
/linewidth 0 def
/home { 150 750 moveto -90 rotate }def
/drawscale 700 def
% Flowsnake:
% /numpt 8 def
% /slst [ 0.0 0.37796 0.37796 0.37796 0.37796 0.37796 0.37796 0.37796 ] def
% /relalst [ -19.1 60.0 120.0 -60.0 -120.0 0.0 -60.0 79.1 ] def
% /backflags [ false false true true false false false true ] def
% /botflags [ false false false false false false false false ] def
% /invflags [ false false false false false false false false ] def
% /leftflags [ true true true true true true true true ] def
% /drawlevel 5 def
% /linewidth 0.5 def
% /home { 100 400 moveto } def
% /drawscale 400 def
% Square snowflake:
% /numpt 9 def
% /slst [ 0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ] def
% /relalst [ 0 90 -90 -90 0 90 90 -90 0 ] def
% /backflags [ false false false false false false false false false ] def
% /botflags [ false false false false false false false false false ] def
% /invflags [ false false false false false false false false false ] def
% /leftflags [ true true true true true true true true true ] def
% /drawlevel 5 def
% /linewidth 0 def
% /home { 300 800 moveto -90 rotate }def
% /drawscale 800 def
% Triangle quilt:
% /numpt 10 def
% /slst [ 0.0 0.47141 0.33333 0.33333 0.33333 0.31427 0.22222 0.22222 0.22222 0.44444 ] def
% /relalst [ 45 -45 180 -270 135 -45 180 -270 90 0 ] def
% /backflags [ false false false false false false false false false false ] def
% /botflags [ false false false false false false false false false false ] def
% /invflags [ false false false false false false false false false false ] def
% /leftflags [ false false false false false false false false false true ] def
% /drawlevel 6 def
% /linewidth 0 def
% /home { 100 750 moveto -90 rotate }def
% /drawscale 700 def
% Tempete (lightning storm):
% /numpt 7 def
% /slst [ 0.0 0.23570 0.16667 0.68718 0.66667 0.33333 0.23570 ] def
% /relalst [ -45 45 76 -166 90 45 -45 ] def
% /backflags [ false false false true true true true ] def
% /botflags [ false false false false false false false ] def
% /invflags [ false false false true true false false ] def
% /leftflags [ true true true false true false false ] def
% /drawlevel 6 def
% /linewidth 0.5 def
% /home { 100 400 moveto } def
% /drawscale 400 def
% Umbrella Tree:
% /numpt 9 def
% /slst [ 0.0 0.65 0.65 0.65 0.65 0.65 0.65 1.3 1.0 ] def
% /relalst [ 72.7 0 -180 0 28.6 0 180 -104.3 0 ] def
% /backflags [ false false false false false false false false false ] def
% /botflags [ false true false true true true false true true ] def
% /invflags [ false true false false false true false false false ] def
% /leftflags [ true false true false false false false false false ] def
% /drawlevel 14 def
% /linewidth 0 def
% /home { 100 400 moveto 300 400 lineto }def
% /drawscale 200 def
% Cacti:
% /numpt 8 def
% /slst [ 0.0 0.27182 0.30469 0.30104 0.30249 0.23633 0.23343 0.26797 ] def
% /relalst [ 4.8 75.4 -162 81.8 83.4 -163.9 74.2 6.3 ] def
% /backflags [ false false false false false false false false ] def
% /botflags [ false false false false false false false false ] def
% /invflags [ false false false false false false false false ] def
% /leftflags [ true true true true true true true true ] def
% /drawlevel 5 def
% /linewidth 0 def
% /home { 80 750 moveto -90 rotate } def
% /drawscale 700 def
% Dragon curve:
% /numpt 5 def
% /slst [ 0 0.5 0.5 0.5 0.5 ] def
% /relalst [ -90 90 90 -90 0 ] def
% /backflags [ false false true false true ] def
% /botflags [ false false false false false ] def
% /invflags [ false false false false false ] def
% /leftflags [ true true true true true ] def
% /drawlevel 7 def
% /linewidth 0 def
% /home { 370 565 moveto -90 rotate } def
% /drawscale 432 def
% Sierpinski arrowhead:
% /numpt 4 def
% /slst [ 0 0.5 0.5 0.5 ] def
% /relalst [ 60 -60 -60 60 ] def
% /backflags [ false false false false ] def
% /botflags [ false false false false ] def
% /invflags [ false false false false ] def
% /leftflags [ true false true false ] def
% /drawlevel 10 def
% /linewidth 0 def
% /home { 50 700 moveto -90 rotate }def
% /drawscale 600 def
% -----------------------------------------------------------------------------
% Format of the input parameters needed for creating your own fractals.
% Note: These parameters are identical to those output by FractaSketch.
% A fractal is represented as a connected sequence of line segments called
% a template. When the fractal is drawn each segment is recursively replaced
% by a scaled-down copy of the template. Each segment of the template
% has 4 single bit attributes that determine how the scaled-down version
% will be drawn.
% Scalar parameters:
% numpt = number of points in the template (equal to number of segments + 1)
% drawlevel = depth of recursion
% linewidth = width of drawing line
% Segment parameters:
% slst = lengths of the segments scaled so the template has horizontal length
% equal to 1. The first element of slst is not used, put zero here.
% relalst = relative angle between this segment and the previous one.
% backflags = true if the segment is drawn backwards.
% botflags = true if recursion stops with this segment.
% invflags = true if drawing of this segment is inverted in color.
% leftflags = true if positive angles are counterclockwise.
% -----------------------------------------------------------------------------
% Turtle graphics utilities:
/circ12 180 def
/left { rotate } def
/right { neg rotate } def
/forward { currentpoint translate { 0 lineto } { 0 moveto } ifelse } def
% -----------------------------------------------------------------------------
% Utilities allowing easy access to the local parameters of
% drawfractal(level, scale, visflag, rightflag, backflag):
% Only use these if there is nothing else on the stack:
/level { 4 index } def
/scale { 3 index } def
/visflag { 2 index } def
/rightflag { 1 index } def
/backflag { dup } def
% Use these when there is junk on the stack;
% give the number of items on the stack as an argument:
/+level { 4 add index } def
/+scale { 3 add index } def
/+visflag { 2 add index } def
/+rightflag { 1 add index } def
/+backflag { index } def
/declevel { 5 -1 roll 1 sub 5 1 roll } def
/5pops { pop pop pop pop pop } def
% -----------------------------------------------------------------------------
% The main definition of drawfractal:
/drawfractal {
level 0 le
{ scale visflag forward }
{ declevel
gsave
level 0 gt
{ backflag
{ scale false forward circ12 left } if
rightflag
{ relalst 0 get right }
{ relalst 0 get left } ifelse
1 1 numpt 1 sub
{ botflags 1 index get
{ slst 1 index get 2 +scale mul
invflags 2 index get forward
}
{ slst 1 index get 2 +scale mul
2 +level exch
3 +visflag invflags 4 index get xor
4 +rightflag leftflags 5 index get xor not
backflags 5 index get
drawfractal
} ifelse
1 +rightflag
{ relalst exch get right }
{ relalst exch get left } ifelse
} for
}
{ backflag
{ scale false forward circ12 left } if
rightflag
{ relalst 0 get right
1 1 numpt 1 sub
{ botflags 1 index get
{ slst 1 index get 2 +scale mul
invflags 2 index get forward
}
{ slst 1 index get 2 +scale mul
2 +visflag invflags 3 index get xor forward
} ifelse
relalst exch get right
} for
}
{ relalst 0 get left
1 1 numpt 1 sub
{ botflags 1 index get
{ slst 1 index get 2 +scale mul
invflags 2 index get forward
}
{ slst 1 index get 2 +scale mul
2 +visflag invflags 3 index get xor forward
} ifelse
relalst exch get left
} for
} ifelse
} ifelse
stroke
grestore
scale false forward
} ifelse
5pops } def
% -----------------------------------------------------------------------------
% Main program
newpath
linewidth setlinewidth
home
currentpoint translate
drawlevel drawscale true false false drawfractal
stroke
showpage