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 on January 27th, 2007

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2 Comments    Leave a comment.

  1. On 12 Feb 2007 at 12:23 alexandra Said:

    Great… I love these posts of yours that I can read and not understand a word at all. I’m feeling like Santa’s little helper then (like in that episode where Bart tries to teach him simple stuff such as ‘sit’) But, uhm, yes, it’s quite fascinating, this formula- has a nice pattern somehow. I could draw a picture of it, might look pretty in a way… By the way- you wrote a new post, waaaaahhh! This is remarkable. Really. I mean it.

  2. On 26 Feb 2010 at 11:44 Simon Said:

    Geil ALTER!

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