Introduction

[Florian]

Guten Tag, Hello and Priviet!

 I'm here because I followed some Thread about 'How the z=z²+c might look in 3D'. (Someone postet a Picture from a Mandelbrot which looked like a simple rotation of the 2D-MBro. Nope ... that was a nice discussion.  )

I finally signed up here, because I'm writing a Fractal-Explorer myself in Java.
Today I spent looking for Qaternions and Octonions but found no Triternions  .

I saw 4 episodes of Chaos-TV at Youtube and was pleased.
 

Wish all here a happy new year.

[cKleinhuis]

hello and welcome to the forums,
the mandelbulb - which is still the most closest thing to a real 3d mandelbrot (the holy grail of fractalists) - has been found here
https://en.wikipedia.org/wiki/Mandelbulb

the idea is quite simple, analog to 2dimensional complex multiplication ( add angles - multiply lengthes ) a second add for the second axis is leading to the mandelbulb

thank you for mentioned chaostv i am pleased to hear that some people get something out of it ( and if its just registering here ) i hope to continue my tutorial about the julia sets in the beginning of next year

[Florian]

Thanks cKleinhuis,

for the hint with the mandelbulb (thougt it was a software).

Thats really very close to that Triternions I was looking for.

 

[cKleinhuis]

We call them triplex numbers here

[lycium]

As far as I know there are only 4 normed division algebras, with dimensions 1, 2, 4 and 8: https://en.wikipedia.org/wiki/Composition_algebra#Structure_theorem

So any algebra made with other dimensions will lack some quite important properties... I guess it doesn't matter too much if you just want to square and add numbers though (rather than stuff like sine, cosine, ... convergent series etc).