generate random points on the surface of a sphere

random_sphere_surface.py

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.pyplot import plot, scatter, imshow
from mpl_toolkits.mplot3d import Axes3D

N = 1000

z = np.random.uniform(-1, 1, N)
phi = np.random.uniform(-np.pi, np.pi, N)
rxy = np.sqrt(1 - z**2)

x = rxy * np.cos(phi)
y = rxy * np.sin(phi)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x, y, z, marker='+')
plt.show()