# Tk_Newton_Raphson_Fractal.py

# Tk_Newton_Raphson_Fractal.py

from tkinter import *
from PIL import Image, ImageTk
from itertools import combinations
from cmath import *

ww = 600
hh = 600

# creates a z**4+1 = 0 fractal using the Newton-Raphson
# root finding method
delta       = 0.000001  # convergence criteria
iters       = 30        # number of iterations

# these are the solutions to the equation z**4+1 = 0 (Euler's formula)
solutions = [cos((2*n+1)*pi/4)+1j*sin((2*n+1)*pi/5) for n in range(4)]
colors = [(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0)]

def draw():
    image.putdata(rgb)
    photo = ImageTk.PhotoImage(image)
    canvas.create_image(0,0,image=photo,anchor=NW)
    canvas.update()


root = Tk()
root.title("Tk_")
root.geometry("%dx%d+0+0"%(ww,hh))

canvas = Canvas(root, width=ww, height=hh)
canvas.pack()

image = Image.new("RGB", (ww,hh), (255,255,255))

rgb = []
for re in range(0, ww):
    for im in range(0, hh):
        z = (re+1j*im)/hh
        for i in range(iters):
            try:
                z -= (z**4+1)/(4*z**3)
            except ZeroDivisionError:
                continue
            if(abs(z**4+1)<delta):
                break

        # color depth is a function of the number of iterations
        color_depth = int((iters-i)*255.0/iters)

        # find to which solution this guess converged to
        err = [ abs(z-root) for root in solutions ]
        distances = zip(err, range(len(colors)))

        # select the color associated with the solution
        color = [i*color_depth for i in colors[min(distances)[1]]]
        rgb.append(tuple(color))
draw()