Archive for January 27th, 2007

Jeff Tupper’s Self-Referential Formula

I’ve always been fascinated with self-referentialism in all its forms, so when I stumbled upon a mathematical formula that can plot itself, I was pretty intrigued.

You take this formula:

\displaystyle\frac12 < \left\lfloor \mathrm{mod} \left( \left\lfloor \frac{y}{17}\right\rfloor 2^{-17\lfloor x\rfloor -\mathrm{mod}(\lfloor y\rfloor , 17)},2\right)\right\rfloor

Which you then run over certain values of x and y, plot the result, and you get:

Plotting result

Pretty fascinating, isn’t it? At least until you figure out how it does what it does, and that it’s really not black magic at all, and that it doesn’t take some freak chance to discover such a beast. But I leave that as an exercise for my readers ;-)

Published in: Uncategorized | on January 27th, 2007 | 1 Comment »