import numpy as np import matplotlib.pyplot as plt from PIL import Image
def Tupper_self_referential_formula(k): aa = np.zeros((17, 106))
def f(x, y): y += k a1 = 2 ** -(-17 * x - y % 17) a2 = (y // 17) // a1 return 1 if a2 % 2 > 0.5 else 0
for y in range(17): for x in range(106): aa[y, x] = f(x, y) return aa[:, ::-1]
k = 9489414856877039590479997730148554425666925984049232945604842888420596111937489062065081199094002132087091572191187170308560128611026043144427876131133135794969867759108490917632153891963456295991713868378392769549376070709924497237322046334486274987407067993824142187115870972520417207510521083293280152434558803258138899515603807505064799735152359900010019631133734298562293682916239050320580346316026460860919542540955914826806059123630945216006606268974979135253968165822806241305783300650874506602000048154282039485531804337171305656252