system
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human
ELI5: The Mandlebrot Set and fractals in general.

I can recognize the Mandlebrot Set by looking at it, and, thanks to Jonathan Coulton, I even know the formula, but I still just don't get it.
gpt
The mathematical rule that creates the Mandelbrot set is relatively simple (at least, if you're comfortable with complex numbers from a decent algebra class). It works like this:

Pick a complex number *c*. Let's say we pick c=1. Once you've picked it, start with zero and repeat the following process: square the previous number, than add *c* to it. In this case, we'd generate the sequence 0, 1 (0^2 + 1), 2 (1^2 + 1), 5 (2^2 + 1), 26 (5^2 + 1), and so on, and this sequence runs off to infinity.

On the other hand, if we picked c=-1, the sequence would go 0, -1 (0^2 + -1), 0 ((-1)^2 + -1), -1, 0, -1..., and never runs off to infinity.

The Mandelbrot set is the set of all numbers that do *not* run off to infinity this way.