# Reproduced from: https://jakevdp.github.io/blog/2013/02/16/animating-the-lorentz-system-in-3d/ 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 lorentz_deriv(X, t0, sigma=10., beta=8./3, rho=28.0): """Compute the time-derivative of a Lorentz system.""" x, y, z = X; 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(lorentz_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 # 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('lorentz_attractor.mp4', fps=15, extra_args=['-vcodec', 'libx264']) plt.show()