% Postscipt implementation of an L-system
%
% Probably a reasonable introduction to PS programming too.
%
% adb@tardis.ed.ac.uk
% Ideas:  Can have multiple rules by creating multiple recurse functions
% (or by making 'recurse' take an argument) eg. recurseY to include another
% rule Y at the current point.
% maxdepth controls the depth of recursion.  We can't set this very high
% in this implementation since we maintain the whole stack.  Example timings
% on a P133 are: 
%    maxdepth = 7 takes 5 secs
%    maxdepth = 8 takes 13 secs
%    maxdepth = 9 takes about 1m30

/maxdepth { 7 } def

%
% Variables affecting L-system drawing
%
% anglestep - how much does a "+" or "-" rotate us by?
% direction - the angle (from horizontal) we start at.
% length - the initial length of a line segment
% start-point - (0,0) is at bottom left

/anglestep 15 def
/direction 30.0 def
/length 150 def
/start_point { 0 0 } def

% Some defines to let us use more traditional rule descriptions
/START { saveposition } def
/END { restoreposition } def
/* { drawline } def
/@ { 0.7 changelength } def
/+ { turnleft } def
/- { turnright } def

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Rules
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/X { START + @ * recurse END START - @ * recurse END  recurse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% End of rules
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 'recurse' is used as part of the rule to indicate that 
% X should be repeated at this point.  Since we don't 
% have infinite memory or time, we only recurse up to maxdepth
/increasedepth { /depth depth 1 add def } def
/decreasedepth { /depth depth 1 sub def } def

/recurse
{
  depth maxdepth lt
  { increasedepth  X  decreasedepth } {} ifelse
} def

% Helpers - convert from angle to horizontal/vertical projection.
/angletohorz { cos } def
/angletovert { sin } def % angle of 45 give 0.707

% Actions
/drawline 
{ 
  direction angletohorz length mul
  direction angletovert length mul
  rlineto 
} def
/turnright       { /direction direction anglestep sub def } def
/turnleft        { /direction direction anglestep add def } def
/saveposition    { direction length currentpoint } def
/restoreposition { moveto /length exch def  /direction exch def } def
/changelength    { /length exch length mul def } def

%
% Start of main code
%
/depth { 0 } def
start_point moveto
X
stroke
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