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Thanks for the Link.
We have a member called Betchen who may help to explain what he is doing, if you email her. She is not very active on the forum but does call by from time to time.

The work Of Ushiki is based as are all complex fractals of this sort , on Trochoids. The shapes i have viewed are sculpted or rather printed as maps of trochoidal paths. Quasz with which i am more famiiar in its user setting, cuts and smooths a quaternion block. It can deal with octonions but i have not bothered to explore those, yet.

This method is a trace method so it is like drawing a line of points to build the surface, rather than fitting a surface to the points where possible.

I mention Trochoids regularly because Laz Plaths app draws them beautifuly and intuitively, and you can see how these traced forms are constructed from rotating circles in the plane.
http://home.comcast.net/~trochoid/TroUV.html

It would be interesting to see some scripts for that!