mandelbrot in imaginary space

hi,
i've extended the complex plane to 3 and 4 dimensions.
i'm sure this has been done before, but just in case...
the unit of the imaginary axis is i. it is the the root of the negated
unit of the real axis.
generalizing to find another orthogonal axis, the unit of another axis
is root(-i). (the root of the negated unit of the imaginary axis)
interestingly, arithmetic in this space uncovers a fourth axis: root(i)
i've got a mandelblob animation with root(i) axis set to zero and
root(-i) axis varying from 0 through 1 (time) at
http://ivorykite.com/4Dmb.html
if anyone's seen this before and/or has some better quality animations
or slices of the mandelbrot, please let me know.
cheers, jack

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