tinkerTieAnimationPlot.py

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
from matplotlib import cm
import matplotlib.animation as animation
import numpy as np
#plt.rcParams['animation.ffmpeg_path'] = 'some directory/ffmpeg-20150317-git-d24af70-win64-static/bin/ffmpeg'
plot_args = {'rstride':1, 'cstride':1, 'cmap':cm.coolwarm, 'linewidth':0, 'antialiased':False}

titleString = r'$z = \frac{1}{(12 \tan^{-1}(\frac{y}{|x|})+ \frac{3\pi}{2}\sin(2\pi t))^2 + 1}$'
fig = plt.figure()
ax = fig.gca(projection='3d')
X = np.arange(-5, 5.25, 0.251)
Y = np.arange(-2, 2.1, 0.101)
X, Y = np.meshgrid(X, Y)

def wings(x, y, t):
	phi = 12*(np.arctan(y/abs(x)) + np.pi/8*np.sin(2*np.pi*t))
	return 1/(phi*phi + 1)

def data_gen(i):
	ax.clear()
	plt.title(titleString)
	plot = ax.plot_surface(X,Y, wings(X,Y,i/30.), **plot_args)
	return plot,

Z = wings(X,Y, 0)
plot = ax.plot_surface(X,Y, Z, **plot_args)

anim = animation.FuncAnimation(fig, data_gen, interval=30, blit=False)

ax.set_zlim(0, 1.01)
plt.title(titleString)

#FFwriter = animation.FFMpegWriter()
#anim.save('Tie1.mp4',fps=30, writer = FFwriter)

plt.show()

I just sort of smashed this code together with the help of examples.