from numpy import cos
from numpy import linspace
import matplotlib.pyplot as plt

plt.style.use('seaborn-v0_8-muted')

def g(u, c, f):
    t = f(u) + c
    
    return 2*u*t**2 / (u**2 + t**2)

def h(u, c, f):
    t = f(u) + c
    return 2*u*u*t / (u**2 + t**2)

t = linspace(-7, 7, 10000)
fig, ax = plt.subplots()
f = lambda x: cos(8*x) 
for c in range(-10, 11):
    ax.plot(g(t, c, f), h(t, c, f))
    plt.axis("off")
plt.show()




t = linspace(-7, 7, 10000)
fig, ax = plt.subplots()
f = lambda x: x 
for c in range(-10, 11):
    ax.plot(g(t, c, f), h(t, c, f))
    plt.axis("off")
plt.show()
# See Mathematics Magazine, v 52 no 3, p175