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A Python program to generate and visualize a Mandelbrot set
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| import numpy as np | |
| import matplotlib.pyplot as plt | |
| ''' | |
| z₀ = 0 | |
| zₙ₊₁ = zₙ² + c | |
| ''' | |
| def is_mandelbrot(complex_num, max_iter=100): | |
| z = 0 | |
| for n in range(max_iter): | |
| z = z**2 + complex_num | |
| if abs(z) > 2: | |
| return False | |
| return True | |
| def generate_mandelbrot_points(resolution=100): | |
| real = np.linspace(-2, 0.8, resolution) | |
| imag = np.linspace(-1.4, 1.4, resolution) | |
| points = [] | |
| for r in real: | |
| for i in imag: | |
| c = complex(r, i) | |
| if is_mandelbrot(c): | |
| points.append(c) | |
| return points | |
| def plot_mandelbrot(points): | |
| real_parts = [p.real for p in points] | |
| imag_parts = [p.imag for p in points] | |
| plt.figure(figsize=(10,10)) | |
| plt.scatter(real_parts, imag_parts,s=1,c="black") | |
| plt.axis("equal") | |
| plt.show() | |
| if __name__ == "__main__": | |
| mandelbrot_points = generate_mandelbrot_points(resolution=100) | |
| print(len(mandelbrot_points), "points in the set") | |
| plot_mandelbrot(mandelbrot_points) | |
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| from PIL import Image | |
| mandelbrot = Image.effect_mandelbrot((1000, 1000), (-3, -2.5, 2, 2.5), 100) | |
| mandelbrot.show() |
200-point resolution
500-point resolution
Pillow Mandelbrot
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100-point resolution