That trick always seemed incomplete to me because the output only contains part of the formula; it's missing the constant that actually encodes most of the information. Has anyone ever made one where the output contains everything you need?
Yes! To both.
Calling Tupper's formula "self-referential" (which he did not) is essentially cheating: https://shreevatsa.wordpress.com/2011/04/12/how-does-tuppers...
But someone has made one where the output contains everything: http://jtra.cz/stuff/essays/math-self-reference/
A little discussion on Reddit: http://www.reddit.com/r/math/comments/i75t1/tuppers_formula_...
Re:The Batman Equation
by burgerbrain on Saturday July 30, 2011 @03:09PM
(#2826419)
If you consider outputs for equations other than Cartesian graphs, then Quines should get you what you want.
Yes, I think a "Cartesian" quine would be pretty tough to create, because you're going from a symbolic representation to an inefficient visual representation. Could a more efficient visual representation solve it? One approach might be to output a bitmap that looks like this:
gunzip(########)
where ######## is a bitmap representation of the raw input to gunzip.
http://en.m.wikipedia.org/wiki/Tuppers_self-referential_form...