Sorry, it ain't self-referential unless it draws the picture around (0, 0).<p>I have no idea if that's possible, though. Quines are possible in many programming languages, but the "language" of formulas without quantifiers is very limited. You can encode boolean logic, not sure about loops.<p>EDIT:<p>After some Googling, I've found a true self-referential formula: <a href="http://jtra.cz/stuff/essays/math-self-reference/index.html" rel="nofollow">http://jtra.cz/stuff/essays/math-self-reference/index.html</a><p>Note that it involves a recursive function definition, and part of the formula is generated by a fixpoint trick. I suppose that's the simplest way to do this.<p>Also I really enjoyed the way he embedded a watermark into the formula, in a way that's difficult to remove if you don't know what you're doing.
Self-referential formulas (truly self-referential ones, not involving the magic constant in Tupper's famous one) are conceptually a consequence of Kleene's recursion theorem, just like self-printing programs, but with a bit more caveats---obviously necessary caveats since it all depends on things like font choice etc. I spelled the details out in a paper [1] but there's really nowhere appropriate to publish it, since it's too trivial for a mathematician/computer scientist audience and too tricky for a more general audience.<p>[1] <a href="http://semitrivial.com/papers/eqn.pdf" rel="nofollow">http://semitrivial.com/papers/eqn.pdf</a>
Numberphile video about this formula: <a href="https://www.youtube.com/watch?v=_s5RFgd59ao" rel="nofollow">https://www.youtube.com/watch?v=_s5RFgd59ao</a>
Tupper, Jeff. "Reliable two-dimensional graphing methods for mathematical formulae with two free variables." Proceedings of the 28th annual conference on Computer graphics and interactive techniques. ACM, 2001.<p><a href="http://www.dgp.utoronto.ca/papers/jtupper_SIGGRAPH2001.pdf" rel="nofollow">http://www.dgp.utoronto.ca/papers/jtupper_SIGGRAPH2001.pdf</a>
2^(106*17) only has 543 decimal-digits. So with a high likelyhood, the formular will plot "this is so wrong" in several basic fonts and languages for smaller n's as an input.
Hm, to me this feels scammy, like the 'my-crack-is-nothing-but-the-32894239487th-prim'-trick. Count me impressed as soon as the plot also contains the input range ;)