Monday, May 7, 2012

Interesting formula...and graph

Have you seen a mathematical formula, when graphed in two dimensions, can exactly reproduce the formula itself visually? Here is one:

               {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.

When proper parameters are chosen for x and y, which at the same time satisfy this inequality, the resulting graph will look like this:

             Tupper's self referential formula plot.png,

which, as you can see, looks exactly the same as the original formula. Interesting, huh?

See more here. HT: Feng Dong.

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