Triternions

[Russell Walsmith]

SeqFans,

This is my first posting to this list; if there are some conventions I've
overlooked in this process, please let me know...

Maybe some on this list will find the 'triternion' numbers to be of
interest. This idea sprung from my observation that the juliabrot fractal (
i.e., the 4-D, quaternion-based Mandelbrot set) was less than satisfying in
3-D. I thought that the cyclic group of order six (C6) could be used to
generate a 3-space M-set, and after some years of refinement, the proof of
concept (the T-set) has arrived at

http://ixitol.com/html/videos.html

I've also delved into other properties of this system of ordered triplets.
It's been an adventure to try to port certain standard mathematical tools
into this somewhat kinky context, and in the process, some interesting
sequences have begun to appear; e.g.,
A112260 = 1, 1, 1, 11, 31, 19, 41, 11, 431, 899, 199, 1349, 1951, 15539,
24119, 5269, 36209, 115939, 522919, 583451, 459649…

More info on this at:

http://ixitol.com/html/triternions.html

Clearly, I've but scratched the surface here, and hopefully others will be
inspired to take up where I've presently left off. If so, if anyone gets
around to writing code that manipulates these numbers, I'd like to see it,
particularly that which runs on Maple 10. Thanks.

Ciao, Russell
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