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I have recently discovered that I can create letters and any shape I want by hiding parts of curves by making them complex. To generalise if I want $x>a$ then I multiply my function by $\sqrt{\frac{|x-a|}{x-a}\,}$ and replacing $x-a$ with $b-x$ I can make $x.

The challenge I put forward is this:

Create an equation or set of equations, which graph the equations themselves

Is this possible?

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    @JordanBrown judging by the looks of the screengrab, you're using the application that comes with os x? have you looked at the examples drop down menu? i think using parametric equations might be a bit simpler (some people might call this cheating)2013-06-20

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As Ross Millikan says in the comments, Tupper's self-referential formula is a famous example.

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    +1, but Tupper's "self-referential" formula (which he never named so, in [the excellent paper where he used it as example](http://www.dgp.toronto.edu/~mooncake/papers/SIGGRAPH2001_Tupper.pdf)) just takes a bitstring (the region) and forms a bitmap out of it. This is like a program that echoes its input: sure, when given its own code as input it does print it out, but that doesn't make it a quine. However, Jakub Trávník has written a true mathematical "quine", whose graph contains all the information necessary to recreate it: [here](http://jtra.cz/stuff/essays/math-self-reference/index.html).2013-06-24