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:

960939379918958884971672962127852754715004339660129306

651505519271702802395266424689642842174350718121267153

782770623355993237280874144307891325963941337723487857

735749823926629715517173716995165232890538221612403238

855866184013235585136048828693337902491454229288667081

096184496091705183454067827731551705405381627380967602

565625016981482083418783163849115590225610003652351370

343874461848378737238198224849863465033159410054974700

593138339226497249461751545728366702369745461014655997

933798537483143786841806593422227898388722980000748404719.

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:

770137614616740349659457383109219250729889213023196245

754997397474539522884572693040838328048207848222847384

255800207585680609541957604841348860558024608884092791

814186507612666983299083984568308963916568266347954249

445046515417964282372279838338100838479512127675315663

107944860681436794491747199511098181076928

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)

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Very clever.

Someone had some fun and made a really self referential formula… http://jtra.cz/stuff/essays/math-self-reference/index.html

Ah, now this is nice. Not going to try and verify it though.

(Also note that I responded to you on the “Cubed” entry.)