I've studiously read through all the posts in this thread and found it all to be be very very interesting. But often, I found myself thinking "oh my god, what what what?"
... To quote some of you:
Another variation in my UF formula is that I added standard escape-time IFS style transforms which can be mixed with the other formula types
"3D/4D forms such as quaternon/hypercomplex/bicomplex"
"complicated 3D formulas actually involving 3D transcendental functions."
I have also enjoyed looking at a hybrid of the standard Trig (real) ( Float power:: 7.4659, z-multiplier: -0.5) with a Bulbox that's pretty much default, each 1 iteration. It's all wicker-y and has twisty stuff and a couple of other features
because of the number of types of conformal transformations available in 3-dimensions is limited (rotations, scaling, inversion, and translation).
the most "sophisticated" 3D factal rendering is being done by those using L-Systems (or at least L-Systems converted to a form of IFS) and that there are other fractal forms (DLA, plasma/fBm,attractors) that work in 3D+.
Also the 4D forms extending from the 3D Mandelbulb have yet to be fully investigated, I fully expect some of those to be more mathematically "consistent" than the 3D, maybe even finding a true "field" ?
So I'd like to know if any of you could point me in the right direction... I'd like to understand the maths behind 3D Mandelbrot/fractals (already have the 2D maths down, mostly
). Once I understand it all, I'll be creating a Tutorial on my own blog. (My goal is to put all the fractal newbie stuff in one place, my blog, as I learn it all myself).
I have been searching for some answers myself but truly, most sites always assume some previous advanced maths knowledge.
... Oh and, I'm posting here to get the attention of all you wise men
.. Let me know if I need to start a new thread somewhere instead.