Actually, I can think of one application for which quaternions and such are not enough: 3D fractals. I will have to find the thread on fractalforums.com, but it describes the creation of the MandelBox and MandelBulb in accessible language but technical detail, as the story of an artist being unsatisfied with quaternions, which take Mandelbrot-type fractals and make them 'look like whipped cream', as they only preserve their ragged nature in one dimension, and the others are something like rotations. So the artist in question figured out something that looked more Mandelbrottish, I forget how, but it might be interesting. -Arlo
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