ds-phasespace-drawing-3D.py

from pylab import *
from mpl_toolkits.mplot3d import Axes3D

def initialize(x0, y0, z0):
    global x, y, z, xresult, yresult, zresult
    x = x0
    y = y0
    z = z0
    xresult = [x]
    yresult = [y]
    zresult = [z]

def observe():
    global x, y, z, xresult, yresult, zresult
    xresult.append(x)
    yresult.append(y)
    zresult.append(z)

def update():
    global x, y, z
    nextx = 0.5 * x + y
    nexty = -0.5 * x + y
    nextz = - x - y + z
    x, y, z = nextx, nexty, nextz

ax = gca(projection='3d')

for x0 in arange(-2, 2, 1):
    for y0 in arange(-2, 2, 1):
        for z0 in arange(-2, 2, 1):
            initialize(x0, y0, z0)
            for t in range(30):
                update()
                observe()
            ax.plot(xresult, yresult, zresult, 'b')

show()