At 07:48 20/05/2002, Gerald K. Dobiasovsky wrote:
From: "Morgan L. Owens" <packrat@nznet.gen.nz>
Quaternions aren't the only way to extend complex numbers. Fractint also provides the other simple four-dimensional alternative, known there as "hypercomplex" numbers. "Simple" is a regrettable lapse into jargon - it would take us too far afield to explain here, but I feel obliged to use it as I just now cooked up a "non-simple" group of four-dimensional numbers. Where hypercomplex numbers have (see Fractint's docs):
ij=ji=k, jk=kj=-i, ki=ik=-j, ii=jj=-kk=-1, ijk=1
and quaternions have
ij=-ji=k, jk=-kj=i, ki=-ik=j, ii=jj=-kk=-1, ijk=-1
These ones I just made have
ij=ji=k, jk=kj=i, ki=ik=j, ii=-jj=-kk=-1, ijk=1
I just had to take a look!
The well known Julia iteration znew = z^2 + c, implemented in, well, Owens Numbers...
Gee, I'm blushing... :-)
I hope you like it.
The depth code in the formula alone makes them worth it. For the pictures themselves, I found myself reminded of photos of asteroids - partly the mood of the pieces, and partly for the air of discovery about them. Morgan L. Owens "There's a world to explore; tales to tell back on shore."