Re: mandelbrot in imaginary space

In article <1119412978.107469.128410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
effbiae <effbiae@xxxxxxxxx> wrote:

> 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
>

In conventional mathematics, the complex plane already contains a
square root of -i, so no extension is needed for this.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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