[onions]

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?

[svat]

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_...

[burgerbrain]

If you consider outputs for equations other than Cartesian graphs, then Quines should get you what you want.

https://secure.wikimedia.org/wikipedia/en/wiki/Quines

[onions]

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.