Heighway dragon fractal recursive implementation in Python

heighway.py

import png #pip3 install pypng
import math

class Heighway:

    def __init__(self, size = 1000):
        self.size = size

    def init_grid(self):
        self.grid = []
        for _ in range(self.size):
            row = []
            for _ in range(self.size):
                row.append(255)
            self.grid.append(row)

    def next(self, x1, y1, x2, y2, k):
        if k > 0:
            xn = (x1 + x2) / 2 + (y2 - y1) / 2
            yn = (y1 + y2) / 2 - (x2 - x1) / 2
            self.next(x2, y2, xn, yn, k-1)
            self.next(x1, y1, xn, yn, k-1)
        else:
            self.bresenham(x1, y1, x2, y2)

    def bresenham(self, xa, ya, xb, yb):
        xa = int(xa)
        ya = int(ya)
        xb = int(xb)
        yb = int(yb)

        dx = abs((int)(xb - xa))
        sx = 1 if xa < xb else -1

        dy = abs((int)(yb - ya))
        sy = 1 if ya < yb else -1

        err = int((dx if dx>dy else -dy)/2)
        e2 = 0

        while True:
            self.grid[ya][xa] = 0
            if xa == xb and ya == yb:
                break
            e2 = err
            if e2 > -dx:
                err -= dy
                xa += sx
            if e2 < dy: 
                err += dx
                ya += sy

    def draw(self, iterations, filename):
        self.init_grid()
        f = open(filename, 'wb')
        w = png.Writer(self.size, self.size, greyscale=True)

        s1 = self.size * 0.3
        s2 = self.size - s1
        self.next(s1, s1, s2, s2, iterations)

        w.write(f, self.grid)
        f.close()


# ----------------------------------------

f = Heighway()
for i in range(22):
    f.draw(i, f'fractal_{i}.png')