# https://realpython.com/mandelbrot-set-python/

from dataclasses import dataclass


@dataclass
class MandelbrotSet:
    max_iterations: int

    def __contains__(self, c: complex) -> bool:
        return self.stability(c) == 1

    def stability(self, c: complex) -> float:
        return self.escape_count(c) / self.max_iterations

    def escape_count(self, c: complex) -> int:
        z = 0
        for iteration in range(self.max_iterations):
            z = z**2 + c
            if abs(z) > 2:
                return iteration
        return self.max_iterations


mandelbrot_set = MandelbrotSet(max_iterations=20)

width, height = 512, 512
scale = 0.0075
GRAYSCALE = "L"

from PIL import Image

image = Image.new(mode=GRAYSCALE, size=(width, height))
for y in range(height):
    for x in range(width):
        c = scale * complex(x - width / 2, height / 2 - y)
        instability = 1 - mandelbrot_set.stability(c)
        image.putpixel((x, y), int(instability * 255))

image.show()