How to draw a fractal image?¶

The Numpy library makes it easy to work with matrices in Python.

Because it is implemented in C, numpy accelerates many calculations. It is also type-safe - all elements of a matrix have the same type. Many of the most powerful Python libraries like pandas, scikit-learn and Pillow have been built on top of numpy.

Install it with:

pip install numpy

The following code draws the Mandelbrot set:

"""
Drawing the Mandelbrot set
based on R code by Myles Harrison
http://www.everydayanalytics.ca
"""
import numpy as np
from PIL import Image

SIZE = 500

x = np.linspace(-2.0, 1.0, SIZE)
y = np.linspace(-1.5, 1.5, SIZE)

ones = np.ones(SIZE)

c = np.outer(x, ones) + 1j * np.outer(ones, y)

z = np.zeros((SIZE, SIZE)) * 1j
k = np.zeros((SIZE, SIZE))

for i in range(100):
    index = np.abs(z) < 2
    z[index] = z[index] ** 2 + c[index]
    k[index] = k[index] + 1


# save the image
im = Image.fromarray(k).convert('RGB')
im.save('mandelbrot.png')