This is Tupper’s Self-Referential Formula:
what makes it interesting is that the set of points , for which the inequality holds, in the rectangle , , you will get this:
Turns out that the graph of the formula resembles the formula itself, which at first sounds pretty incredible. Oh, wait: I didn’t specify the value of n. It should be equal to:
Read more about it in Wikipedia.
I spent a couple of evenings trying to figure out how does it work, and intended to write a long post about it, but I see that it has already been done here much better than I could, so I’ll only give you the main idea: the graph of the formula contains all possible combinations of pixels of size and what you need to do is to locate the right fragment of the graph by choosing the value of n. Fortunately, the formula is constructed in such a way that it can be done rather easily. For instance, if you set n to be equal to:
you will get a fragment of the graph saying “hello world!”. (Oh, and it will be upside down, as pointed out in the blog post I already mentioned)