Sierpinski

Sierpinski’s triangle and friends

import numpy as np
import matplotlib.pyplot as plt
np.random.seed(0)


def sierpinski(n_vert, n_iter, **kwargs):
    vertices = [
        np.array([np.cos(theta), np.sin(theta)])
        for theta in np.pi/2 + np.linspace(0, 2*np.pi, n_vert, endpoint=False)
    ]
    pos = vertices[0]

    history = []
    for i in range(n_iter):
        destination = vertices[np.random.randint(0, n_vert)]
        delta = destination - pos
        pos = pos + delta/2
        history.append(pos)

    data = np.stack(history)

    fig, ax = plt.subplots()
    plt.scatter(data[:, 0], data[:, 1], s=1, **kwargs)
    ax.set_aspect('equal')
    return fig

sierpinski(n_vert=3, n_iter=5000).show()

sierpinski(n_vert=5, n_iter=200000, alpha=0.1).show()

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