A computer graphics student of mine, around 1985, made some pictures of the quaternionic Mandelbrot set as his term project. They certainly *appeared* more complicated than the ordinary M. set. But it's true that any non-real quaternion, together with 1, spans a complex subspace of the quaternions, whose arithmetic is identical to the complex numbers, and so would give the usual Mandelbrot set. (Using the standard definition, non-commutativity plays no role.) So the different appearance of the quaternionic M. set might be due to its being a 4D object that was projected to 3D in order to view it. (Can *that* be what the cool computer graphics are doing?) --Dan ------------- Gareth wrote: << It's alleged (on a page linked to from the one we're talking about) that the obvious quaternionic generalization of the Mandelbrot set is basically the ordinary Mandelbrot set plus some rotational symmetry and has no "extra" fractal structure to it. This seems plausible enough on the face of it, but I've not made any attempt to check. I share your feeling that it's all a bit ad hoc and humdrum, and that it should be possible to get as much or more aesthetic beauty with more mathematical elegance.

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele