Self-Referential Formula: Math Equation That Plots Itself!

The above equation is a math formula concocted by J. Tupper - what's amazing is that when you plug in a certain value, the formula plots a self-referential graph that is ... itself! Link - via reddit


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You can't "plug in" a "certain value" anywhere, as there are no free variables. All this does is describe an infinitely large image full of utter garbage, and if you look in just the right location, you find the above image.

Conceptually, that thing is super simple and by far not as impressive as a quine. And school children can make quines.

But what's cool about it is that someone has actually found a combination of a pixel-formula and just the right location in its output, the one piece of garbage that looks like the original pixel-formula. You see, you could have a computer just scroll through random formulas until it detects an image that looks right, but if you have a look at the Y coordinate at which you find Tupper's graphic ... that thing has over 500 digits! Trying out so many combinations would take for-fucking-ever! I don't mean forever as in "at this altitude it takes forever to boil an egg". I mean forever as in "I wonder if this calculation has any chance of finishing before the cold death of the universe."

So ... how did Tupper do this? Does anyone know?
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