#!/usr/bin/env python
# coding: utf-8

# In[4]:


from mpmath import mp
import numpy as np
import matplotlib.pyplot as plt

get_ipython().run_line_magic('pylab', 'inline')


# [Tupper's formula](https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula)
# 
# $$ \frac{1}{2} < \left \lfloor{ \text{mod}\left ( \left \lfloor{\frac{y}{17}} \right \rfloor 2^{-17 \lfloor{x}\rfloor - \text{mod} \left ( \lfloor{y}\rfloor, 17 \right )} \right ) } \right \rfloor $$

# In[167]:


mp.prec = 2000


# In[180]:


def tupper_field(k):
    field = np.ndarray((17,106), np.bool)
    for xix, x in enumerate(mp.arange(0,106)):
        for yix, y in enumerate(mp.arange(k,k+17)):
            t1 = mp.floor(y) % 17
            t2 = -17*mp.floor(x)
            t3 = 2**(t2 - t1)
            t4 = mp.floor(y/17)
            t5 = (t4 * t3) % 2
            field[16-yix, xix] = 0.5 < mp.floor(t5)
    return field


# In[181]:


k1 = mp.mpf('820959624942020445814005879832445494830930')
k2 = mp.mpf('4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300')


# In[182]:


for k in [k1,k2]:
    f = tupper_field(k)
    ax = plt.imshow(f, cmap='Greys', interpolation='nearest')
    ax.axes.axis('off')
    plt.show()