Don't think this is going to work as a straight out number system.. rather it's a system of rotations being calculated algebraically, rather than trigonometrically, which might not be too useful....

A new number system based on the 3d fractal formula I posted in the

"search for the holy grail" thread that generates images for z^2, such as this one:

In this system components are divided into planar and linear components as follows:

x, y, and z are the linear components.

w, v, and u are the planar components.

w is the planar component that relates to the linear component x.

w is the planar magnitude of the y-z plane: w= sqrt(y^2 + z^2)

v is the planar component that relates to the linear component y.

v is the planar magnitude of the x-z plane: w= sqrt(x^2 + z^2)

u is the planar component that relates to the linear component z.

u is the planar magnitude of the x-y plane: w= sqrt(x^2 + y^2)

The planar triplex z is noted in this way:

z

*1*= [ (x

*1*,w

*1*) ; (y

*1*,v

*1*) ; (z

*1*,u

*1*) ]

z

*2*= [ (x

*2*,w

*2*) ; (y

*2*,v

*2*) ; (z

*2*,u

*2*) ]

Addition and subtraction follow the same basic format, here is an addition:

z

*1* + z

*2* = [(x

*1*+x

*2*,w

*1*+w

*2*) ; (y

*1*+y

*2*,v

*1*+v

*2*) ; (z

*1*+z

*2*,u

*1*+u

*2*)

Multiplication and division follow slightly different basic formats, here is a multiplication:

First, we take the magnitude of the system:

~~|~~*q*| = |z*1* & z*2* *| = sqrt(x*1**x*2* + w*1**w*2* + y*1**y*2* + v*1**v*2* + z*1**z*2* + u*1**u*2*)

Updated magnitude information will be here later today.

Then we calculate new components:

x

*1*2* = |

*q*| * (x

*1**x

*2* - w

*1**w

*2*) / (x

*1**x

*2* + w

*1**w

*2*)

w

*1*2* = |

*q*| * (x

*2**w

*1* + x

*1**w

*2*) / (x

*1**x

*2* + w

*1**w

*2*)

y

*1*2* = |

*q*| * (y

*1**y

*2* - v

*1**v

*2*) / (y

*1**y

*2* + v

*1**v

*2*)

v

*1*2* = |

*q*| * (y

*2**v

*1* + y

*1**v

*2*) / (y

*1**y

*2* + v

*1**v

*2*)

z

*1*2* = |

*q*| * (z

*1**z

*2* - u

*1**u

*2*) / (z

*1**z

*2* + u

*1**u

*2*)

u

*1*2* = |

*q*| * (z

*2**u

*1* + z

*1**u

*2*) / (z

*1**z

*2* + u

*1**u

*2*)

Division will come later. Movie night...

Here is an image of a z^13 quadrant of the new formula (all positives for planes, I like the positive quadrant, can set planes according to corresponding xyz signs in order to have 8 different quadrants, but I am still exploring the positive):

I guess I should include the corresponding z^2 positive quadrant: