Pyplot how to plot math art

Take the first example in the reported link:

enter image description here

So you have to do a for loop with k from 1 to N = 14000, in each iteration you draw a circle of radius R and center in (X, Y) defined in the above equations:

N = 14000

for k in range(1, N + 1):
    X = cos(10*pi*k/N)*(1 - 1/2*(cos(16*pi*k/N))**2)
    Y = sin(10*pi*k/N)*(1 - 1/2*(cos(16*pi*k/N))**2)
    R = 1/200 + 1/10*(sin(52*pi*k/N))**4

At this point you have the coordinates of the circle's center and its radius, but not the circle iteself yet, so you you have to compute it. First of all you have to define an angle theta from 0 to 2*pi, then compute the cirle's points with:

N = 14000
theta = np.linspace(0, 2*pi, 361)

for k in range(1, N + 1):
    X = cos(10*pi*k/N)*(1 - 1/2*(cos(16*pi*k/N))**2)
    Y = sin(10*pi*k/N)*(1 - 1/2*(cos(16*pi*k/N))**2)
    R = 1/200 + 1/10*(sin(52*pi*k/N))**4

    x = R*np.cos(theta) + X
    y = R*np.sin(theta) + Y

Finally, you can draw the circles in each iteration.

Complete code

import numpy as np
import matplotlib.pyplot as plt
from math import sin, cos, pi


N = 14000
theta = np.linspace(0, 2*pi, 361)

fig, ax = plt.subplots(figsize = (10, 10))

for k in range(1, N + 1):
    X = cos(10*pi*k/N)*(1 - 1/2*(cos(16*pi*k/N))**2)
    Y = sin(10*pi*k/N)*(1 - 1/2*(cos(16*pi*k/N))**2)
    R = 1/200 + 1/10*(sin(52*pi*k/N))**4

    x = R*np.cos(theta) + X
    y = R*np.sin(theta) + Y

    ax.plot(x, y, color = 'blue', linewidth = 0.1)

plt.show()

enter image description here