# tk_cubic_golden_ratio.py

# tk_cubic_golden_ratio.py

import tkinter as tk
import math

def create_cube(size):
    r = size / 2
    points = [
        (0, -r),
        (r * math.cos(math.pi/6), -r * math.sin(math.pi/6)),
        (r * math.cos(math.pi/6), r * math.sin(math.pi/6)),
        (0, r),
        (-r * math.cos(math.pi/6), r * math.sin(math.pi/6)),
        (-r * math.cos(math.pi/6), -r * math.sin(math.pi/6))
    ]
    points[1] = (points[1][0]*0.8, points[1][1]*1.2)
    points[2] = (points[2][0]*0.8, points[2][1]*1.2)
    points[4] = (points[4][0]*0.8, points[4][1]*1.2)
    points[5] = (points[5][0]*0.8, points[5][1]*1.2)
    return points

def place_tile(x, y, angle, points):
    rotated = []
    for px, py in points:
        rx = px * math.cos(angle) - py * math.sin(angle)
        ry = px * math.sin(angle) + py * math.cos(angle)
        rotated.append((x + rx, y + ry))
    color = "#{:02x}{:02x}{:02x}".format(
        int(255 * (0.5 + 0.5 * math.sin(angle))),
        int(255 * (0.5 + 0.5 * math.sin(angle + 2.1))),
        int(255 * (0.5 + 0.5 * math.sin(angle + 4.2))))
    canvas.create_polygon(rotated, fill=color, outline="black", width=1)

def create_cubic_golden_ratio(x, y, size):
    points = create_cube(size)
    max_radius = (ww**2 + hh**2)**0.5 + size
    tile_spacing = size * 0.302
    golden_angle = math.pi * (3 - math.sqrt(5))  # ~137.5 degrees

    radius = 0
    n = 1
    while radius < max_radius:
        radius = math.sqrt(n) * tile_spacing

        angle = n * golden_angle
        tx = x + radius * math.cos(angle)
        ty = y + radius * math.sin(angle)
        n += 1

        place_tile(tx, ty, angle + math.pi/2, points)

ww, hh = 600, 600
root = tk.Tk()
root.geometry(f"{ww}x{hh}+0+0")
canvas = tk.Canvas(root, width=ww, height=hh)
canvas.pack()

create_cubic_golden_ratio(ww//2, hh//2, 50)
print('done.')

root.mainloop()