from PIL import Image WIDTH = 1000 HEIGHT = 1000 LIMIT = WIDTH * HEIGHT img = Image.new("RGB", (WIDTH, HEIGHT)) pixels = img.load() def collatz_pixel(n: int): x = n even_count = 0 odd_count = 0 max_value = x if x == 1: seq = [1, 4, 2, 1] even_count = sum(1 for v in seq if v % 2 == 0) odd_count = sum(1 for v in seq if v % 2 == 1) max_value = max(seq) else: while True: if x % 2 == 0: even_count += 1 x //= 2 else: odd_count += 1 x = 3 * x + 1 if x != 1 else 1 if x > max_value: max_value = x if x == 1: odd_count += 1 break r = min(even_count, 255) g = min(odd_count, 255) b = min(max_value // n, 255) return (r, g, b) for n in range(1, LIMIT + 1): px = (n - 1) % WIDTH py = (n - 1) // WIDTH pixels[px, py] = collatz_pixel(n) img.save("collatz.png", "PNG") print("Saved image")