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Tupper's Self-Referential Formula

1 pointsby isomorphabout 1 year ago

1 comment

moritzwarhierabout 1 year ago
Has been discussed many times for sure, but is still nice :)<p>Notably, the formula basically just has any possible permutation of &quot;pixels&quot; of the given length in its output space, not just the chosen one.<p>In a way it is a mathematically encoded version of the &quot;Infinite monkey theorem&quot; and not really a quine (but can be considered one if you blink and embed the right number)<p>&gt; The formula is a general-purpose method of decoding a bitmap stored in the constant k {\displaystyle k}, and it could be used to draw any other image. When applied to the unbounded positive range 0 ≤ y {\displaystyle 0\leq y}, the formula tiles a vertical swath of the plane with a pattern that contains all possible 17-pixel-tall bitmaps. One horizontal slice of that infinite bitmap depicts the drawing formula itself, but this is not remarkable, since other slices depict all other possible formulae that might fit in a 17-pixel-tall bitmap. Tupper has created extended versions of his original formula that rule out all but one slice.<p>The &quot;self-referential&quot; part of the name is a bit of a gimmick, could as well call it Tuppers formula.