# tk_FFT_Fractal.py

# tk_FFT_Fractal.py

import tkinter as tk
from PIL import Image, ImageTk
import math

W = 600
H = 600
root = tk.Tk()
root.title("# tk_FFT_Fractal.py")
root.geometry("+0+0")
canvas = tk.Label(root)
canvas.grid(row=0, column=0, columnspan=3)

gradient = Image.new('RGB', (3, 3))
pixels = gradient.load()
grid_colors = {
    (0, 0): (255, 255, 255),  # White
    (0, 1): (255, 255, 0),    # Yellow
    (0, 2): (0, 255, 0),      # Green
    (1, 0): (255, 165, 0),    # Orange
    (1, 1): (128, 128, 128),  # Gray
    (1, 2): (0, 0, 255),      # Blue
    (2, 0): (255, 0, 0),      # Red
    (2, 1): (128, 0, 128),    # Purple
    (2, 2): (0, 0, 0)         # Black
}
for x in range(3):
    for y in range(3):
        pixels[x, y] = grid_colors[(x, y)]
gradient = gradient.resize((W, H))
color_cache = {}
for x in range(W*2):
    dx = x
    for y in range(H*2):
        dy = y
        if x >= W:
            x = 2*W - 1 - x
        if y >= H:
            y = 2*H - 1 - y
        color_cache[(dx, dy)] = gradient.getpixel((x, y))

scale = 0.0025

freqs = [3.0, math.pi, math.pi/3]
amplitudes = [1.1, 1.2, 1.3]

dbl = W*2
def fft_fractal_iter(cx, cy):
    x = cx
    y = cy

    for i in range(len(amplitudes)):
        x_new = x*x - y*y + cx * 0.5
        y_new = 2*x*y + cy * 0.5

        x_new += math.sin(x * freqs[i % len(freqs)]) * amplitudes[i % len(amplitudes)]
        y_new += math.cos(y * freqs[i % len(freqs)]) * amplitudes[i % len(amplitudes)]

        x = x_new
        y = y_new

    color_x = int(abs(x * W))
    color_y = int(abs(y * W))

    return color_cache[(color_x % dbl, color_y % dbl)]

img = Image.new("RGB", (W, H))
def draw_frame():
    p = img.load()
    zoom = scale

    for py in range(H):
        for px in range(W):
            cx = (px - W/2) * zoom
            cy = (py - H/2) * zoom

            color = fft_fractal_iter(cx, cy)
            p[px, py] = color

    tkimg = ImageTk.PhotoImage(img)
    canvas.configure(image=tkimg)
    canvas.img = tkimg

draw_frame()
root.mainloop()