lorenz attractor

https://github.com/rebeccabilbro/viz/blob/master/animation/lorenz_animation.py

import numpy as np
from scipy import integrate

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import cnames
from matplotlib import animation

N_trajectories = 20


def lorenz_deriv((x, y, z), t0, sigma=10., beta=8./3, rho=28.0):
"""Compute the time-derivative of a Lorenz system."""
return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]


# Choose random starting points, uniformly distributed from -15 to 15
np.random.seed(1)
x0 = -15 + 30 * np.random.random((N_trajectories, 3))

# Solve for the trajectories
t = np.linspace(0, 4, 1000)
x_t = np.asarray([integrate.odeint(lorenz_deriv, x0i, t)
for x0i in x0])

# Set up figure & 3D axis for animation
fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')
ax.axis('off')

# choose a different color for each trajectory
colors = plt.cm.jet(np.linspace(0, 1, N_trajectories))

# set up lines and points
lines = sum([ax.plot([], [], [], '-', c=c)
for c in colors], [])
pts = sum([ax.plot([], [], [], 'o', c=c)
for c in colors], [])

# prepare the axes limits
ax.set_xlim((-25, 25))
ax.set_ylim((-35, 35))
ax.set_zlim((5, 55))

# set point-of-view: specified by (altitude degrees, azimuth degrees)
ax.view_init(30, 0)

# initialization function: plot the background of each frame
def init():
for line, pt in zip(lines, pts):
line.set_data([], [])
line.set_3d_properties([])

pt.set_data([], [])
pt.set_3d_properties([])
return lines + pts

# animation function. This will be called sequentially with the frame number
def animate(i):
# we'll step two time-steps per frame. This leads to nice results.
i = (2 * i) % x_t.shape[1]

for line, pt, xi in zip(lines, pts, x_t):
x, y, z = xi[:i].T
line.set_data(x, y)
line.set_3d_properties(z)

pt.set_data(x[-1:], y[-1:])
pt.set_3d_properties(z[-1:])

ax.view_init(30, 0.3 * i)
fig.canvas.draw()
return lines + pts

Writer = animation.writers['ffmpeg']
writer = Writer(fps=15, metadata=dict(artist='Rebecca'), bitrate=1800)

# instantiate the animator.
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=500, interval=30, blit=False)

# Save as mp4. This requires mplayer or ffmpeg to be installed
anim.save('lorenz_attractor.mp4', writer=writer)

# plt.show()