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Tupper's Self-Referential Formula

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Tupper's formula

J. Tupper concocted the amazing formula

1/2<|_mod(|_y/(17)_|2^(-17|_x_|-mod(|_y_|,17)),2)_|,

where |_x_| is the floor function and mod(b,m) is the mod function, which, when graphed over 0<=x<=105 and n<=y<=n+16 with

n=96093937991895888497167296212785275471500433 966012930665150551927170280239526642468964284217 435071812126715378277062335599323728087414430789 132596394133772348785773574982392662971551717371 699516523289053822161240323885586618401323558513 604882869333790249145422928866708109618449609170 518345406782773155170540538162738096760256562501 698148208341878316384911559022561000365235137034 387446184837873723819822484986346503315941005497 470059313833922649724946175154572836670236974546 101465599793379853748314378684180659342222789838 8722980000748404719,

gives the self-referential "plot" illustrated above.

Tupper's formula can be generalized to other desired outcomes. For example, L. Garron (pers. comm.) has constructed generalizations for n=13 to 29.

See also

Self-Recursion

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References

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, p. 289, 2007."Self-Answering Problems." Math. Horizons 13, No. 4, 19, Apr. 2005.Wagon, S. Problem 14 in http://stanwagon.com/wagon/Misc/bestpuzzles.html.

Referenced on Wolfram|Alpha

Tupper's Self-Referential Formula

Cite this as:

Weisstein, Eric W. "Tupper's Self-Referential Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html

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