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"""
References:
    1. http://linas.org/art-gallery/escape/escape.html
    2. https://www.codingame.com/playgrounds/2358/how-to-plot-the-mandelbrot-set
"""

from math import log2
from PIL import Image, ImageDraw
from typing import Tuple

escape_radius = 20.0
max_iter = 20
image_size = (600, 600)
origin = (450, 300)
zoom = 200


def mandelbrot(c: complex) -> float:
    z = complex(0)
    iter_count = 0
    while iter_count < max_iter and abs(z) <= escape_radius:
        z = z * z + c
        iter_count += 1

    return iter_count if iter_count == max_iter else iter_count - log2(log2(abs(z)))


def colormap_lookup(mu) -> Tuple[int, int, int]:
    hue = int(255 * mu / max_iter)
    saturation = 255
    value = 255 if mu < max_iter else 0
    return hue, saturation, value


def main():
    img = Image.new("HSV", image_size, (0, 0, 0))
    draw = ImageDraw.Draw(img)

    for x in range(0, image_size[0]):
        for y in range(0, image_size[1]):
            c = complex((x - origin[0]) / zoom, (y - origin[1]) / zoom)
            mu = mandelbrot(c)
            draw.point([x, y], colormap_lookup(mu))

    img.show()


if __name__ == "__main__":
    main()