But unfortunately, I have yet to even begin to understand how it all works. Hell, I'm not even sure about how, in 2D fractals, i=sqrt(-1) ... This simply seems impossible to me, yet it all works when the maths is applied. I have a feeling that if I truly do want to understand such things, I would need to take a few steps back, go restudy the last few years of High School maths and then continue on to University level maths. But there's no way I can do that. The idea actually entices me because I've always loved mathematics and problem solving. So when it's combined with concepts like eternity and chaos, I REALLY get interested, but for now and for the foreseeable future, I just don't have the time.
But, for anyone who cares to try on their own, here's the Mandelbulb formula from Daniel White's site (One of the original discoverers of the 3D MAndelbulb). I tried using this as a starting point to further discover how it all worked, and failed:
What's the formula of this thing?
There are a few subtle variations, which mostly end up producing the same kind of incredible detail. Listed below is one version. Similar to the original 2D Mandelbrot, the 3D formula is defined by:
z -> z^n + c
...but where 'z' and 'c' are hypercomplex ('triplex') numbers, representing Cartesian x, y, and z coordinates. The exponentiation term can be defined by: