#!/usr/local/bin/perl
#
#  Author:   Mitch Richling<http://www.mitchr.me>
#  IP:       Copyright 1994 by Mitch Richling.  All rights reserved.
#  Key word: lorenz strange attractor povray Euler
#  Notes:    This is a very simple program to generate a curve based
#            on Lorenz's attractor.  It uses Euler's method to solve the
#            equations.  The "curve" consists of a series of spheres
#            placed at each point found on the curve.  The spheres
#            are connected with cylinders.  Note that this program 
#            is simple enough to be coded with Povray itself.  This
#            Perl version is much shorter than the C version.

$maxBalls = 10000;
$tDelta = 0.01;
$x = 0.1;
$y = 0.0;
$z = 0.0;
$a = 10.0;
$b = 28.0;
$c = 8.0 / 3.0;
printf(STDERR "Computation starting...\n");
printf("sphere {<%f,%f,%f>, %f texture { crvTex } }\n", $x, $y, $z, 0.2);
      
for($numBalls=0;$numBalls<$maxBalls;$numBalls++) {
  $xNew = $x + $a*($y-$x)*$tDelta;
  $yNew = $y + ($x*($b-$z)-$y)*$tDelta;
  $zNew = $z + ($x*$y-$c*$z)*$tDelta;
  
  if(($numBalls % int($maxBalls/20)) == 0) {
    printf(STDERR "Step: %6d  tDelta: %15.3f x: %15.2f y: %15.2f z: %15.2f\n", $numBalls, $tDelta, $x, $y, $z);
  }
  
  printf("sphere {<%f,%f,%f>, %f texture { crvTex } }\n", $xNew, $yNew, $zNew, 0.1);
  printf("cylinder {<%f,%f,%f>, <%f,%f,%f>, %f texture { crvTex } }\n", $x, $y, $z, $xNew, $yNew, $zNew, 0.2);
  
  $x=$xNew;
  $y=$yNew;
  $z=$zNew;
}