import argparse


def fractal(size: int, depth: int, g2: float, g3: float):
    xi = yi = -2
    xf = yf = 2

    code = ""
    for y in range(size):
        zy = y * (yf - yi) / (size - 1) + yi
        for x in range(size):
            zx = x * (xf - xi) / (size - 1) + xi
            z = zx + zy * 1j
            for i in range(depth):
                if abs(z) > 2:
                    code += str(i)
                    break
                z = (z**4 + 0.5 * g2 * z * z + 2 * g3 * z + 1 / 16 * g2**2) / (
                    4 * z**3 - g2 * z - g3
                )
    return code


def main():
    parser = argparse.ArgumentParser()
    parser.add_argument("--size", "-s", type=int, default=128, required=False)
    parser.add_argument("--depth", "-d", type=int, default=8, required=False)
    parser.add_argument("-g2", type=float, default=0.0, required=False)
    parser.add_argument("-g3", type=float, default=1.0, required=False)

    args, _ = parser.parse_known_args()

    code = fractal(args.size, args.depth, args.g2, args.g3)
    print(code)


if __name__ == "__main__":
    main()