Here is the Lorenz attractor both in 3D and animated. The script is in the following link (along with many goodies) in Jake VanderPlas' Pythonic Perambulations. You can learn a lot by going line-by-line through the script - it's an elegant use of matplotlib objects.
https://jakevdp.github.io/blog/2013/02/16/animating-the-lorentz-system-in-3d/
I added these two lines just before return in the animate function, and then used ImageJ to import the "image stack" and save the "animated GIF":
fname = "Astro_Jake_" + str(i+10000)[1:]
fig.savefig(fname)
Here is Jake's original with two small modifications https://pastebin.com/qWkLft0K (the blit=True used to be necessary for me on macOS but it doesn't seem to be any more)
- get rid of the explicit tuple inside
lorenz_deriv() and unpack it in the lines below
- add a True/False toggle - either it makes a nice animation in real time, or it saves ~1000 small .png files for later building a GIF.
Here is a minimal, simplified example of plotting lines in 3D based on the above:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from scipy.integrate import odeint as ODEint
def lorentz_deriv(xyz, t0, sigma=10., beta=8./3, rho=28.0):
"""Compute the time-derivative of a Lorentz system."""
x, y, z = xyz # unpack here
return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]
x = np.linspace(0, 20, 1000)
y, z = 10.*np.cos(x), 10.*np.sin(x) # something simple
fig = plt.figure()
ax = fig.add_subplot(1,2,1,projection='3d')
ax.plot(x, y, z)
# now Lorentz
times = np.linspace(0, 4, 1000)
start_pts = 30. - 15.*np.random.random((20,3)) # 20 random xyz starting values
trajectories = []
for start_pt in start_pts:
trajectory = ODEint(lorentz_deriv, start_pt, times)
trajectories.append(trajectory)
ax = fig.add_subplot(1,2,2,projection='3d')
for trajectory in trajectories:
x, y, z = trajectory.T # transpose and unpack
# x, y, z = zip(*trajectory) # this also works!
ax.plot(x, y, z)
plt.show()
