import pygame
from random import *

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 = [0, s]
B = [s, s]
C = [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 = [randrange(breite+1), randrange(hoehe+1)]

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

    zufall = randrange(3)
    Q = liste_eckpunkte[zufall]
    P = [(P[0]+Q[0])/2, (P[1]+Q[1])/2]

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