# LorenzODE.2d.py: The Lorenz chaotic attractor in non-interactive 2D.
#       Note the use of the Euler integration method.
#    This version adapted to use matplotlib, since the original
#    used Visual Python, which appears to have problems with the
#    math computing lab networking.

# Import plotting routines
from pylab import *

# Set up initial condition
x = -10.0
y = -7.0
z = 35.0
# Horizonal and vertical 2D plot projections
xt = []
yt = []

dt = 0.001
sigma = 10.0
R = 28.0
b = -8.0/3.0
theta = 3.0 * pi / 4.0  # Rotate about z-axis

for t in arange(0,10,dt):
  dxdt = sigma * (-x + y)
  dydt = R*x - x*z - y
  dzdt = b*z + x*y
  x = x + dxdt*dt
  y = y + dydt*dt
  z = z + dzdt*dt
  # Rotate orientation in 3D for a better view
  #   about z-axis
  x_rot = cos(theta) * x - sin(theta) * y
  y_rot = sin(theta) * x + cos(theta) * y
  xt.append(x_rot)
  yt.append(z)

# Setup the plot
xlabel('x(t)+y(t)') # set x-axis label
ylabel('z(t)') # set y-axis label
# Set plot title
PlotTitle = 'Lorenz ODE with (sigma,b,R) = (%5.2f,%5.2f,%5.2f)' % (sigma,b,R)
title(PlotTitle)
# Plot the time series
plot(xt,yt, 'k-')
# Make sure the orbit appears in a unit square
axis('equal')
axis([-30.0, 30.0, 0.0, 60.0])

# Use command below to save figure
#savefig('LorenzOrbit', dpi=600)

# Display the plot in a window
show()