4D “Squarry” Julia and Mandelbrot Sets

Julia : c={-0.2,0.8,0,0}, imax=12

{x,y,z,w}2 = {x2-y2-z2-w2, 2(xy+zw), 2(xz+yw), 2(xw-yz)}
David Makin suggested this formula to me for squaring a 4D hypercomplex number.

Link : Mandy Squarry, Minibrot Squarry – by David Makin

Mandelbrot Set, imax=12

Minibrot, imax=20

2 Responses to “4D “Squarry” Julia and Mandelbrot Sets”

  1. 1 giancarlo reali
    February 23, 2011 at 2:51 pm

    hi paul;
    this is the first time i meet your blog.
    i am using mathematica 8, and i tried to run your ‘two-gears’ example;
    it gives back the following error warn:
    LinearSolve::luc: “Result for LinearSolve of badly conditioned matrix {<>} may contain significant numerical errors.”
    can you help me? i suppose you had it perfectly running when you posted it.

  2. 2 Emanuele
    June 21, 2011 at 10:29 pm

    Hello Paul,
    You can try use Golden Bi-quaternion in fractal 8D ?
    Golden bi-quaternion are bi-quaternions satisfying the golden condition Q-1/Q=1


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