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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?

@mathr I tried Julias but they didn't look very good

@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

@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 cool idea! do share the results :)

@mathr Will do!

very noisy because it's just a single pass but it looks like there's some interesting shapes in there

@mathr Wow, okay, I'm having a lot of fun with this!

Did you come up with the idea of looping through functions like this or is there more literature about this out there?

I'm playing with writing a bunch of functions and letting the program choose a few on startup and seeing what happens

claude@mathr@post.lurk.orgAnother good iteration loop formula is:

```

z := z^p + c

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

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

z := z^p + c

```

(p = 2)