#!/usr/bin/perl -Wall

# ================================================================
# John Kerl
# kerl at math dot arizona dot edu
# 2006-10-11
# ================================================================

# ----------------------------------------------------------------
# Simulation parameters

$tmax = 10.0;
$h    = 0.002;
$N    = int($tmax/$h);

# $h    = 0.002;
# $N    = 5000;
# $tmax = $h * $N;

# ----------------------------------------------------------------
# Initial conditions

$x0  = 10.0;
$y0  =  0.0;
$z0  = 10.0;

# ----------------------------------------------------------------
# Functional parameters

$s = 10.0;
$r = 28.0;
$b = 2.666667;

# ----------------------------------------------------------------
# Output parameters

if (@ARGV >= 2) {
	$h = $ARGV[1];
	$N = int($tmax/$h);
}

# ----------------------------------------------------------------
# Integration

$x = $x0;
$y = $y0;
$z = $z0;

for ($t = 0; $t < $tmax; $t += $h) {

	printf "%11.8f\t%11.8f\t%11.8f\n", $x, $y, $z;

	# Cheesy Euler integrator.
	$xp = $s * ($y - $x);
	$yp = $r * $x - $y - $x * $z;
	$zp = $x * $y - $b * $z;

	$x += $h * $xp;
	$y += $h * $yp;
	$z += $h * $zp;
}