Renders a pretty Mandelbrot set using Python. Created for PiCymru. Note that this script requires NumPy and PIL (Python Imaging Library). Tested using Python 3 on Raspbian OS, and Windows 10/11 (Anaconda).

Mandelbrot.py

# Python Mandelbrot set for PiCymru

# This version uses the Python Imaging Library AND NumPy
from PIL import Image
import numpy

WIDTH = 512
HEIGHT = 512
MAX_ITER = 25  # How many iterations to perform z=z2+c

pix = numpy.zeros((HEIGHT, WIDTH, 3), dtype=numpy.uint8)

# For each pixel in our little display...
for y in range(0, HEIGHT):
    for x in range(0, WIDTH):
        zoom = 0.3

        # The z in the mandelbrot set is an imaginary number, made up of
        # a real number and an imaginary component
        real = (float(x) / float(WIDTH)) * (1.0 / zoom) + -2.1 
        imaginary = (float(y) / float(HEIGHT)) * (1.0 / zoom) + -1.6

        # This is the constant, which is the 'c' element of the main equation (z=z2+c)	
        const_real = real
        const_imaginary = imaginary        
        z2 = 0.0
        
        for iteration in range(0, MAX_ITER):
            temp_real = real

            # Calculate z=z2+c
            real = (temp_real * temp_real) - (imaginary * imaginary) + const_real
            imaginary = 2.0 * temp_real * imaginary + const_imaginary
            z2 = real * real + imaginary * imaginary

            # If z2 exceeds 4.0 before we hit MAX_ITER then we exit the loop and the current pixel
            # does not belong to the mandelbrot set
            if z2 > 4.0:
                break

        # Plot the current pixel. If it's in the mandelbrot set then do nothing.
        if z2 > 4.0:            
            c = iteration * 15 % 255            
            if c > 50:
                pix.itemset((y,x,2), c)
            else:
                pix.itemset((y,x,2), 50)

mandelbrot = Image.fromarray(pix, 'RGB')
mandelbrot.save("mandelbrot.png")