from vpython import *
from numpy import arange, clip
# David Scherer
scene.caption = """Right button drag or Ctrl-drag to rotate "camera" to view scene.
Middle button to drag or Alt-drag to zoom in or out.
On a two-button mouse, middle is left + right."""
scene.title = "Lorenz differential equation"
scene.center = vector(25,0,0)
scene.background = color.white
scene.forward = vector(0,-.2,-1)
scene.range = 35
lorenz = curve( color = color.black, radius=0.3 )
# Draw grid
for x in arange(0,51,10):
box(pos=vector(x,0,0), axis=vector(0,0,50), height=0.4, width=0.4, color=color.gray(0.6) )
for z in arange(-25,26,10):
box(pos=vector(25,0,z), axis=vector(50,0,0), height=0.4, width=0., color=color.gray(0.6) )
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.x + y.y*y.z,
- 10*y.y + 10*y.z,
- y.y*y.x + 28*y.y - y.z );
y = y + dydt*dt
# Draw lines colored by speed
c = clip( [mag(dydt) * 0.005], 0, 1 )[0]
lorenz.append( pos=y, color=vector(c,0, 1-c) )
rate( 500 )