Actually that just gave me an idea with respect to quaternions - if one modified their math slightly such that the rotational angle around the real axis itself were a fractal (rather than a smooth circle) this could produce the ultimately "correct" 3D analog of the 2D Mandelbrot maybe even for plain z^2+c. Making the angle fractal is not a approach I've considered previously (or seen elsewhere) ;) On 31 May 2014, at 10:04, David Makin wrote:
Argh, I was correct the first time - in the rotattoinal case (quaternion) as I said the surface around the real; axis is not fractal so the points that would make it 3D from the 2D cross-section *are not surface points*. This also answer's James' point I think/
On 31 May 2014, at 00:41, Warren D Smith wrote:
Just rotate the 2D Mandelbrot set to get a body of revolution with a 3D boundary given that the 2D set has 2D boundary.
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