File:Butterfly catastrophe animation.webm

from mpl_toolkits import mplot3d import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation

video_length = 10 # in seconds video_fps = 30 num_frames = video_fps * video_length angle_per_frame = (360 / num_frames)

stride = 8 width = 1

a = np.linspace(-width, width, 600) b = a x, y = np.meshgrid(a, b) z = -20*x**5 + 4*x**3 - 2*y*x - 0.5 * (x**4 + y**4)

plt.tick_params(left = False) fig = plt.figure(figsize= (10,10)) ax = plt.axes(projection ='3d') frame = ax.plot_wireframe(x, y, z, color ='#4a5a90', rstride=stride, cstride=stride)

def scale(i):

   k = (i / num_frames * np.pi)
   return (1-np.cos(k))/2 * num_frames

1. k = (i / num_frames - 0.5) * 10
2. return (np.tanh(k)+1)/2 * num_frames

def init():

   ax.set_box_aspect((1,1,1))
   ax.view_init(0, 0)
   ax.axis('off')    
   ax.set_xlim(-0.2,0.2)
   ax.set_ylim(-0.2,0.2)
   ax.set_zlim(-0.1, 0.1)
   return frame,

1. animation function. This is called sequentially

def animate(i):

   ax.view_init(0, 0 + angle_per_frame * scale(i))
   return frame,

1. call the animator. blit=True means only re-draw the parts that have changed.

anim = animation.FuncAnimation(fig, animate, init_func=init,

                              frames=num_frames, blit=True)

anim.save('butterfly.mp4', fps=video_fps, extra_args=['-vcodec', 'libx264'])

plt.show()