Python Mandelbrot fractal

README.md

Python Mandelbrot fractal

Trivial implementation of the Mandelbrot fractal written in pure Python. It outputs to the terminal using 24-bit ANSI escape codes, which is widely supported by many terminals.

No optimization was done to the code. It's supposed to be simple and straightforward.

There is a one-to-one mapping between each calculated point from the fractal and one output character. This results in a low-resolution image made of characters (instead of pixels), but it is simple to implement, simple to understand, and widely portable/compatible.

This code is compatible with Python 3 and greatly benefits from running it inside PyPy.

mandelbrot.py

#!/usr/bin/env python3

import argparse
import doctest

def float_range(start, end, steps):
    """Similar to numpy.linspace(), but written in pure Python.

    Extreme cases:

    >>> list(float_range(-5, 5, 0))
    []
    >>> list(float_range(-5, 5, 1))
    [-5.0]

    More useful cases:

    >>> list(float_range(-5, 5, 2))
    [-5.0, 5.0]
    >>> list(float_range(-5, 5, 3))
    [-5.0, 0.0, 5.0]
    >>> list(float_range(-5, 5, 5))
    [-5.0, -2.5, 0.0, 2.5, 5.0]

    >>> list(float_range(0, 2, 5))
    [0.0, 0.5, 1.0, 1.5, 2.0]
    >>> list(float_range(0, 3, 4))
    [0.0, 1.0, 2.0, 3.0]

    Also in reverse order:

    >>> list(float_range(5, -5, 5))
    [5.0, 2.5, 0.0, -2.5, -5.0]
    """
    if steps <= 0:
        return
    if steps == 1:
        yield start * 1.0
        return
    for i in range(steps):
        yield start + (end - start) * (i / (steps - 1))


def mandelbrot_0(c, iters):
    z = c
    nv = 0
    for i in range(iters):
      if abs(z) > 2:
        break
      z = z * z + c
      nv += 1
    return nv


def calculate_mandelbrot(width, height, iters):
    for y in float_range(-1, 1, height):
        for x in float_range(-1.5, 0.5, width):
            c = mandelbrot_0(complex(x, y), iters)
            rgb = round(c / iters * (256 ** 3 - 1))
            print('\033[48;2;{r};{g};{b}m '.format(
                r=round((rgb >> 16) & 0xFF),
                g=round((rgb >>  8) & 0xFF),
                b=round((rgb >>  0) & 0xFF),
            ), end='')
        print('\033[m')


def main():
    parser = argparse.ArgumentParser(
        prog='Mandelbrot in the terminal',
        # Don't add `-h` and `--help`, because it conflicts with `--height`.
        add_help=False,
    )
    parser.add_argument('--help', action='help', help='Show this help message')
    parser.add_argument('-t', '--test', action='store_true', help='Run tests')
    parser.add_argument('-v', '--verbose', action='store_true', help='Verbose test output')
    parser.add_argument('-w', '--width', type=int, default=80, help='Width, in number of characters')
    parser.add_argument('-h', '--height', type=int, default=25, help='Height, in number of lines')
    parser.add_argument('-i', '--iterations', type=int, default=5000, help='Height, in number of lines')
    args = parser.parse_args()

    if args.test:
        doctest.testmod(verbose=args.verbose)
    else:
        calculate_mandelbrot(args.width, args.height, args.iterations)


if __name__ == "__main__":
    main()

screenshot.png