(a^x)^y does not equal a^(x^y)...

...and if you do it the wrong way in your algorithm you do not get the pretty fractal you hoped for...

please excuse my dear aunt Sally

❄️wotitdo❄️ : for what? I mean, if she's a neo-Nazi, crypto-fascist scumbag who eats manatees for breakfast, I'm not excusing any Sally, regardless of whose aunt she might be!

if there's a connection between the crypto-fascists and the crypto-bros.

not aware of the crypto-bros, so I really don't know

there is a connection. Crypto-bros are the people who promote cryptocurrency and other block chain related technologies (none of which I've seen as being good).

they're probably self-serving sociopaths, then, but not necessarily cyrto-fascist.

so here's the fractal:

not done that one (as far as I recall).

imagine Z^Z^Z^... where Z is complex. As for the Mandelbrot set, a starting value of Z might, after some number of iterations, go to a constant value, enter a cycle of some number of steps or "escape" to infinity.

here, starting values of Z that remain finite are coloured black (as is typical for the Mandelbrot set). Other colours all escape, the brighter the colour the faster they do so.

for the Mandelbrot set, |Z| > 4 is proven to escape to infinity, so you can check for that condition and curtail your iterations accordingly. In this case, I have not been able to find any analogous threshold being referred to. (I haven't checked the technical literature).

that should be |Z|^2 > 4 or |Z| > 2.

in the image, the real axis is along the horizontal line of mirror symmetry.

the imaginary axisis harder to locate: The origin is to the left of the two large central overlapping ovals (black). There's a structure that looks like a crab facing viewer's right, seen from above. It seems to be holding a smaller version of itself. The Origin is in the "head" of the "crab".

Maths Makes Monster Crabs

Lemongrass :

they don't seem that monstrous to me, though.