These are all single-function renders, just trying out new functions

Anyone know of a good source of functions that produce Mandelbrot-like fractals?
I need functions that I could essentially hotswap instead of z²+c and have nice results

Kind of gutted I didn't note down which formulae I used here, I'd love to render #4 with more passes

Found it!
It's (zr-zi*i)²+c
So essentially the Mandelbrot function but the complex number has it's imaginary part flipped

@gaeel mathr.co.uk/kf/manual.html#for are the ones in Kalle's Fraktaler 2 (which I am the current maintainer/author of). Most were added by Karl (the original author) based on suggestions from various members of FractalForums (historically .com, currently .org).

But these are all structured like $z→f(z)+c$ (because it needs this format for deep zooming with perturbation rendering), while putting the $c$ elsewhere in the formula can be interesting too.

Also, KF doesn't do formulas with division or functions like $\sin(z)$.

@mathr hey thanks!
I also saw your reply on the Discord

I'm thinking of selecting a bunch of functions and then using words as seeds for the function loops, so I could make pictures associated with words
Not sure how I'd use them, but it's the idea I'm playing with right now

@mathr And yeah, I got some interesting shapes messing with putting c elsewhere, like (z+c)²+c and z^(1+|c|*3)+c

@gaeel complex power to real number like your second example is problematic as it is multi-valued (not a function). Picking just one branch (eg the principal square root branch for power 3/2) can lead to visible discontinuities...

@mathr Not sure I understand what the problem is

I like what the results look like

@gaeel a pity! from the symmetry I guess at power 4 stuff?

@mathr Yeah, probably
I haven't deleted the function, but I need to go through all of the functions I've written to find which one(s) it was

@gaeel make your tool write every setup as you render.

@floatvoid Currently it prints the setup to console, but I should make it output a text file too

@gaeel run it from a script that pipes to a log file. zero work win!

@floatvoid Ahahah, I guess? The log file is really spammy though because it's always printing status updates

@gaeel great! not power 4, sorry for the red herring. this is also called Tricorn or Mandelbar

@mathr No worries! I'd already gone down that path when you mentioned it, so no harm done!

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