One would think that like in the physical world, there should be many "species" with different types of appearances. Each a beautiful system on its own, but in comparable complexity.
Maybe the complexity of the Mandelbrot set is to the mathematical universe what is the complexity of life in the physical universe. Something that is very rare. For some unknown reason.
This wikipedia page has a bunch of examples of Julia sets
https://en.wikipedia.org/wiki/Julia_set#Examples
I'm also partial to Newton fractals, some of which look very cool
Nothing compares to the complexity of the Mandelbrot formula when it comes to colorizing the two-dimensional plane.
With complexity I mean the human impression of complexity. The reaction of "Oh, there is a lot of stuff going on in there" after looking at some parts of it.
Often less, in that the Mandelbrot set has much more regularity than those examples.
I suppose we have different aesthetics.
Even the generalised Mandelbrot fractal formula starts to do this plane-filling via compounding 'branch cuts' in the 'lake'/inside areas when the exponent (a complex number) is a negative non-integer like -1.5+0.0i instead of the usual 2.0+0.0i.
Here's an example I tried to add to Wikipedia but unfortunately it was rejected:
https://commons.m.wikimedia.org/wiki/File:AlanTIsVeryHelpful...
Could be an illusion that it's actually filling the plane, but if so it's an illusion I'm rather fond of!
If you want to show the world a new fractal, I think the best way is to write a js+webgl program and put it online, so people can explore it themselfes.
There's something I'd be much more keen to show the world (and which might render faster than negmandel!) which I call 'mandelfield', here's an old blogger post about it (yeah sorry it's blogger@): https://ultraiterator.blogspot.com/2009/10/hidden-mandelfiel...
And I think Flickr is the best way to browse my fractals at present: https://www.flickr.com/photos/57934548@N02/ My avatar pic there is a 'mandelfield'. I think it's a really interesting phenomena!