Tupper’s self-referential formula #whoa

by David Ng

Learning about this has made my brain quietly implode.

“Tupper’s self-referential formula is a self-referential formula defined by Jeff Tupper that, when graphed in two dimensions, can visually reproduce the formula itself. It is used in various math and computer science courses as an exercise in graphing formulae.

Specifically (From Wikipedia):

The formula is an inequality defined by:

{1\over 2} < \left\lfloor \mathrm{mod}\left(\left\lfloor {y \over 17} \right\rfloor 2^{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2\right)\right\rfloor

where \lfloor \cdot \rfloor denotes the floor function and mod is the modulo operation.

Let k equal the following:


If one graphs the set of points (x,y-k) with 0 \le x \le 106 and k \le y \le k + 17 such that they satisfy the inequality given above, the resulting graph looks like this: