"""
Adapted from Flash 5 movie by jtarbell, March 2001,
levitated.net, based on the work of Ed N. Lorenz

by K. Urner, Oregon Curriculum Network, November, 2001
"""

import math, coords, povray

class Lorentz:

    def __init__(self,iterations=2000,x0=0,y0=-2,z0=-1):
            self.num = iterations
            # initialize seed
            # strange thing is, these numbers can be just about anything
            # yet they will always converge on an identical solution set
            self.x0 = x0
            self.y0 = y0
            self.z0 = z0
            self.depths = {}
            self.outfile = povray.Povray("lorentz2.pov",cf=25.0,cx=0,cy=0, bgcolor="Gray")
            self.outfile.sphcolor = "Blue"

    def run(self):
            # lorentz constants - don't change these
            h = 0.01
            a = 10.0
            b = 28.0
            c = 8.0/3.0
        
            x0 = self.x0
            y0 = self.y0
            z0 = self.z0

            n = 0
            
            while (n < self.num):
               n += 1                
               # lorentz linear function set
               x1 = x0 + h *  a*(y0-x0)
               y1 = y0 + h * (x0*(b-z0) - y0)
               z1 = z0 + h * (x0*y0 - c*z0)
               # solution becomes next seed
               x0 = x1
               y0 = y1
               z0 = z1               
               # write sphere to Povray file
               v = coords.Vector([x0,y0,z0])
               v = v*0.1 # re scale
               self.outfile.point(v)

            self.outfile.close()