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

Another 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)

@mathr What's happening here?
Is this like Mandelbrot fractals except you use a different formula for each step of the iteration?

@gaeel yes that's it: the second one has first iteration Mandelbrot, then two iterations of Burning Ship, then one more iteration of Mandelbrot, then repeat the 4 steps in a loop until the pixel escapes (or you give up).

@mathr Here's my first output
very noisy because it's just a single pass but it looks like there's some interesting shapes in there

Yeah, this is that (mandel, ship, ship, mandel) loop, and I like it!

@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


@gaeel I can't take credit, the idea came from someone on the "Fractal Chats" Discord server who was experimenting with Xaos (which has a syntax that is not optimal for this kind of thing).

Sign in to participate in the conversation

Welcome to, an instance for discussions around cultural freedom, experimental, new media art, net and computational culture, and things like that. This is part of a family of services that include mailing lists, group chat, and XMPP.