Information regarding the Bristorbrot and Doug Bristor's complex rotational maths

http://www.fractaldimension.org.uk/voldsitemirror/**Different Complex Numbers**With the understanding that [imaginary number i] can be represented by rotation of 90° about the origin. I defined [imaginary number j] as a rotation of 90° about the origin and a rotation of 90° with respect to

*.*

So with this in mind I picked up a cube, to help me visualise the rotations, and then recorded the results.

I rotated it upwards 90° *, then following it by turning it a different 90° backwards [j], I defined the result:*

i × j = -j

Then starting again

I rotated 90° backwards [j], followed by 90° upwards *. This gave me the result:*

j × i = i

It is the use of these results when applied into the [Mandelbrot algorithm], that produce the [Bristor set]. Imaginary numbers in additional dimensions can be derived by substituting in the new number in the above equations.

http://code.google.com/p/fractaldimension/

The java code includes 4D and 5D functions

but here is my original 3D algorithm

i.j = -j

j.i = i

public int iterate3D(double rec,double imc, double jmc,int max)

{ double re,im,re2,im2,jm,jm2,ij,tmp;

int itr=0;

double mag=.0;

im=re=jm=re2=im2=jm2=.0;

do {

ij=im*jm;

tmp=re2-im2-jm2+rec;

im=2.0f*im*re-ij+imc;

jm=2.0f*jm*re+ij+jmc;

re=tmp;

re2=re*re;

im2=im*im;

jm2=jm*jm;

itr++;

if (itr>max) break;

mag=re2+im2+jm2;

} while (4.0f>mag );

return itr;

}

Bristorbrot

*rendered by Jos Leys*