Tupper's Self-Referential Formula

DOWNLOAD Mathematica Notebook 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.

Wolfram Web Resources

Mathematica »

The #1 tool for creating Demonstrations and anything technical.

Wolfram|Alpha »

Explore anything with the first computational knowledge engine.

Wolfram Demonstrations Project »

Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

Computerbasedmath.org »

Join the initiative for modernizing math education.

Online Integral Calculator »

Solve integrals with Wolfram|Alpha.

Step-by-step Solutions »

Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own.

Wolfram Problem Generator »

Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.

Wolfram Education Portal »

Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.

Wolfram Language »

Knowledge-based programming for everyone.