Time for action – drawing Lissajous curves

The Lissajous figures are determined by four parameters: A, B, a, and b. Let's set A and B to 1 for simplicity:

1. Initialize t with the linspace() function from -pi to pi with 201 points:

   a = 9
   b = 8
   t = np.linspace(-np.pi, np.pi, 201)

2. Calculate x with the sin() function and np.pi:

   x = np.sin(a * t + np.pi/2)

3. Calculate y with the sin() function:

   y = np.sin(b * t)

4. Plot as shown in the following:

   plt.plot(x, y)
   plt.title('Lissajous curves')
   plt.grid()
   plt.show()

   The result for a = 9 and b = 8 is as follows:

   

What just happened?

We plotted the Lissajous curve with the aforementioned parametric equations where A=B=1, a=9, and b=8. We used the sin() and linspace() functions, as well as the NumPy pi constant (see lissajous.py):

import numpy as np
import matplotlib.pyplot as plt


a = 9
b = 8
t = np.linspace(-np.pi, np.pi, 201)
x = np.sin(a * t + np.pi/2)
y = np.sin(b * t)
plt.plot(x, y)
plt.title('Lissajous curves')
plt.grid()
plt...