Inspired by: https://matplotlib.org/matplotblog/posts/animated-fractals/

julia_set_with_gif.py

import numpy as np
import matplotlib.pyplot as plt
import gif

def julia_quadratic(zx, zy, cx, cy, threshold):
    z = complex(zx, zy)
    c = complex(cx, cy)
    for i in range(threshold):
        z = z**2 + c
        if abs(z) > 4.:
            return i
    return threshold - 1

x_start, y_start = -2, -2
width, height = 4, 4
density_per_unit = 200
re = np.linspace(x_start, x_start + width, width * density_per_unit )
im = np.linspace(y_start, y_start + height, height * density_per_unit)
threshold = 20
n_frames = 100
r = 0.7885
a = np.linspace(0, 2*np.pi, n_frames)

@gif.frame
def plot(i):
    X = np.empty((len(re), len(im)))
    cx, cy = r * np.cos(a[i]), r * np.sin(a[i])
    for i in range(len(re)):
        for j in range(len(im)):
            X[i, j] = julia_quadratic(re[i], im[j], cx, cy, threshold)
    plt.figure(figsize=(10, 10))
    plt.imshow(X.T, interpolation="bicubic", cmap='magma')
    plt.xticks([])
    plt.yticks([])

frames = []
for i in range(n_frames):
    frame = plot(i)
    frames.append(frame)

gif.save(frames, 'julia_set.gif', duration=50)