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I can't remember what it was, but I vaguely remember a semi-famous equation that when graphed spells a math word like "equation" or a number, does anyone know what that is?

GaneGoe
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1 Answers1

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I believe you may be looking for Tupper's self-referential formula :

$$ \frac{1}{2} < \left\lfloor\text{mod}\left( \left\lfloor \frac{y}{17} \right\rfloor 2^{-17\lfloor x\rfloor - \text{mod}(\lfloor y\rfloor, 17)} , 2\right)\right\rfloor$$

This formula plots any bitmap of 105 by 16 in the range $0 \le x \le 16$ and $k\le y\le k+16$, indexed by $k$.

For a particular 543-digit number, it plots itself (upside down), but there exists a $k$ such as it plots equation, number or anything else you'd want to see.

PbWO4
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  • Is there any practical use for this kind of equation? Like does anyone use it for communications or computer graphics or anything like that? – GaneGoe Aug 31 '18 at 11:57
  • Not that I'm aware of. I vaguely recall that $k$ is actually a simple encoding of the bitmap drawing, so it would be way more efficient to just send $k$ and decode it manually. – PbWO4 Aug 31 '18 at 12:08