import pygame
from random import *
import numpy as np

s = 800
breite = s
hoehe = s

weiss = (255, 255, 255)
schwarz = (0, 0, 0)
rot = (255, 0, 0)

pygame.init()
fenster = pygame.display.set_mode((breite+1, hoehe+1))
pygame.display.set_caption("Das Chaos-Spiel")

A = np.array([0, s])
B = np.array([s, s])
C = np.array([s // 2, round(s-3**0.5/2*s)])

liste_eckpunkte = [A, B, C]

fenster.fill(schwarz)
pygame.draw.polygon(fenster, rot, liste_eckpunkte, width=2)
pygame.display.update()

P = np.array([randrange(breite+1), randrange(hoehe+1)])

ende = False
i = 0
while not ende:
    fenster.set_at((round(P[0]),round(P[1])), weiss)   
    i=i+1
    if i % 1000 == 0:
        pygame.display.update()
        i = 0

    zufall = randrange(3)
    Q = liste_eckpunkte[zufall]
    P = (P+Q)/2

    for ereignis in pygame.event.get():
        if ereignis.type == pygame.QUIT:
            ende = True
pygame.quit()