Point.py

import math

class Point:
    def __init__(self, number, root_degree):
        self.number = number
        self.root_degree = root_degree
        self.curr_number_of_iterations = 0
        self.has_converged = False

    def iterate(self, num_of_iterations=1):
        if self.number == 0:
            return
        if self.has_converged:
            return

        for iteration in range(num_of_iterations):
            self.number = (1.0 / self.root_degree) * ((self.root_degree - 1) * self.number + 1.0/pow(self.number, self.root_degree - 1))
            self.curr_number_of_iterations += 1
            self.has_converged = self.__has_converged()

            if self.has_converged:
                break

    def __has_converged(self):
        test = abs(pow(self.number, self.root_degree))

        return abs(test - 1) < 1e-4

    def get_color(self):
        shade = 1 - math.atan(self.curr_number_of_iterations / (self.root_degree * 20)) / (math.pi / 2)
        #shade = (1 - self.curr_number_of_iterations/100.0) ** 2

        red = int((1 + self.number.real) * 127 * shade)
        green = int((1 + self.number.imag) * 127 * shade)
        blue = int(150 * shade)

        if red > 255 or green > 255 or red < 0 or green < 0 or not self.has_converged:
            red = green = blue = 0

        return (red, green, blue)