Tupper’s Self-Referential Formula

Thanks to Nelly Cheboi for bringing this formula, and all the accompanying links, to our attention.

In his humorous 2015 Numberphile video, Matt Parker discusses a remarkable formula by Jeff Tupper of the University of Toronto whose graph is the letters, numbers, and symbols in the formula itself.  More precisely, this formula:

eq.1(1)produces this graph:

Screenshot 2016-05-16 12.18.13

To find out how it’s done, check out Parker’s video, plus this background explanation and generalization by Shreevatsa R. You can use Tupper’s formula to plot your own name (or anything else you like) using this Python code provided by Kaito Einstein.

(image courtesy of Weisstein, Eric W. “Tupper’s Self-Referential Formula.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html)


About Matthew Simonson

I am a second-year Network Science doctoral student at Northeastern University in Boston. I model homophily and time-varying dynamics on social networks.
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1 Response to Tupper’s Self-Referential Formula

  1. Omar Antolín Camarena` says:

    I’d say that Tupper’s formula isn’t self-referential at all. You need to know what domain to plot and a specification of the proper domain doesn’t fit in the resulting plot. Jakub Travnik created a truly self-referential formula: http://jtra.cz/stuff/essays/math-self-reference/index.html

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