halton_sequence.py

import matplotlib.pyplot as plt

"""
The Halton sequence is a generalization of the one-dimensional Van der Corput
sequence.

https://en.wikipedia.org/wiki/Halton_sequence
https://en.wikipedia.org/wiki/Van_der_Corput_sequence
"""


def van_der_corput(n, base=2):
    q = 0
    bk = 1. / base
    while n > 0:
        q += (n % base) * bk
        n //= base
        bk /= base
    return q


def main():
    s1 = [van_der_corput(i, base=2) for i in range(1, 257)]
    s2 = [van_der_corput(i, base=3) for i in range(1, 257)]

    fig = plt.figure()
    ax = fig.add_subplot()
    ax.scatter(s1, s2)
    ax.set_xlabel('x')
    ax.set_ylabel('y')
    fig.tight_layout()
    fig.show()
    plt.close(fig)


if __name__ == '__main__':
    main()