import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import ArtistAnimation
fig = plt.figure()
def circle_func(x_centre_point, y_centre_point, r, n):
    x = np.zeros(n)
    y = np.zeros(n)
    for i in range(0, n, 1):
        alpha = np.linspace(0, 2*np.pi, n)
        x[i] = x_centre_point + r * np.cos(alpha[i])
        y[i] = y_centre_point + r * np.sin(alpha[i])
    return x, y
thetas = np.linspace(0, 4*np.pi, 100)
r = 1
cycloid_x = r * (thetas - np.sin(thetas))
cycloid_y = r * (1 - np.cos(thetas))
x_centre_move = r * thetas
anim_list = []
n = 100
for i in range(0, n, 1):
    x, y = circle_func(x_centre_move[i], r, r, n)
    circle, = plt.plot(x, y, 'g-', lw=2)
    cycloid, = plt.plot(cycloid_x[:i+1], cycloid_y[:i+1], 'r-', lw=2)
    point, = plt.plot(cycloid_x[i], cycloid_y[i], 'bo', markersize=4)
    anim_list.append([circle, cycloid, point])
ani = ArtistAnimation(fig, anim_list, interval=50)
plt.axes().set_aspect('equal')
ani.save('anim.gif')