Sample complex numbers that are not in the Mandelbrot set

nonmandelbrot_set.py

import numpy as np


def make_non_mandelbrot_set(nsamples: int, max_iterations: int) -> np.ndarray:
    """Generate a set of complex numbers that are not in the Mandelbrot set.

    This employs some of the optimizations from this page,
    http://en.wikipedia.org/wiki/Mandelbrot_set#Optimizations

    In order to minimize run time, we are trying to reduce the number of points
    that we already know that are in the mandelbrot set. Points inside the within the
    cardioid and in the period-2 bulb can be eliminiated.

    Args:
        nsamples (int): Number of samples to generate.
        max_iterations (int): Maximum number of iterations to perform.

    Returns:
        np.ndarray: Array of complex numbers that are not in the Mandelbrot set.
    """

    non_mandels = np.zeros(nsamples, dtype=np.complex128)
    n_non_mandels = 0

    cardioid = (
        np.random.random(nsamples) * 4 - 2 + (np.random.random(nsamples) * 4 - 2) * 1j
    )

    p = (((cardioid.real - 0.25) ** 2) + (cardioid.imag ** 2)) ** 0.5
    cardioid = cardioid[cardioid.real > p - (2 * p ** 2) + 0.25]

    cardioid = cardioid[((cardioid.real + 1) ** 2) + (cardioid.imag ** 2) > 0.0625]

    z = np.copy(cardioid)

    for _ in range(max_iterations):
        z = z ** 2 + cardioid

        mask = np.abs(z) < 2
        new_non_msets = cardioid[~mask]
        non_mandels[n_non_mandels : n_non_mandels + len(new_non_msets)] = new_non_msets
        n_non_mandels += len(new_non_msets)

        cardioid = cardioid[mask]
        z = z[mask]

    return non_mandels[:n_non_mandels]