#fractals #graphics #monochrome #art

An excerpt from the parameter plane of this formula iterated in a loop (p = 2):

````

z := z^p + c

z := (|x| - i y)^p + c

z := (x - i |y|)^p + c

```

Is this like Mandelbrot fractals except you use a different formula for each step of the iteration?

@mathr Nice!

Mind if I try running it through my Nebulabrot renderer tonight?

@gaeel oh ok. I've done some Nebulabrot/Buddhabrot stuff in the past, it's fun to have more than 3 channels to map to RGB later.

it's probably not surprising that it's not so interesting with Julia technique, because the Julia set is invariant under iteration, and the filled-in Julia set mostly goes to a periodic attractor (well, there are some aperiodic ones for the Burning Ship I think, see https://math.stackexchange.com/questions/3234950/bounded-aperiodic-orbits-in-the-burning-ship )

gaeel@gaeel@merveilles.town@mathr No, I meant when I do the Nebula-style rendering of Julia (c constant, z_0 set to pixel) fractals, it doesn't give particularly pretty results

The way the Nebulabrot is rendered is you record all the points you visited while iterating, and you brighten those pixels if you escaped, it's a heat-map of the escape paths, rather than a map of which values escape