from visual import *

print """
Right button drag to rotate view.
Left button drag up or down to move in or out.
"""
scene.title = "Lorenz differential equation"
scene.center = vector(25,0,0)
##scene.lights = [ ((0.25, 0.5, 1.0, 0.), (0.6,0.6,0.6)),
##                 ((-1.0, 0.25, -0.5), (0.2,0.2,0.2)) ]

lorenz = curve( color = color.black, radius=0.3 )

# Draw grid
for x in arange(0,51,10):
    curve( pos = [ (x,0,-25), (x,0,25) ], color = (0,0.5,0), radius = 0.3 )
    #box(pos=(x,0,0), axis=(0,0,50), height=0.4, width=0.4)
for z in arange(-25,26,10):
    curve( pos = [ (0,0,z), (50,0,z) ], color = (0,0.5,0), radius = 0.3 )
    #box(pos=(25,0,z), axis=(50,0,0), height=0.4, width=0.4 )

dt = 0.01
y = vector(35, -10, -7)

for t in arange(0,10,dt):
  # Integrate a funny differential equation
  dydt = vector( - 8.0/3*y[0]           + y[1]*y[2],
                              - 10*y[1] +   10*y[2],
                 -  y[1]*y[0] + 28*y[1] -      y[2] );
  y = y + dydt*dt

  # Draw lines colored by speed
  c = clip( [mag(dydt) * 0.005], 0, 1 )[0]

  lorenz.append( pos=y, red=c, blue=1-c )

  rate( 500 )