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My my! How things have changed in a few short weeks!

As i promised i have a few suggestions about the so called handedness term

                         ijyz + jizy

To be plotable ij and ji have to take on values from the following set
                      
                        {1, -1,i, -i,j, -j}

Setting out the possibilities in table form to facilitate exploration:

if ij =	1	-1	i	-i	j	-j
ji may =	1	i	-i	j	-j	i
or	-j	-1	1	i	-i	j
or	-i	j	i	-j	-1	1
or	j	-i	-j	-i	1	-1
or	-1	-j	j	1	j	-i
or	i	1	-1	-1	i	-j

 

Or an alternative layout

if ij =	1  -1    i   -i    j   -j
ji may =	1   1    1   1   1   1
or	-1  -1  -1  -1  -1  -1
or	i     i     i     i    i    i
or	-i    -i   -i    -i   -i   -i
or	j     j     j     j    j    j
or	-j    -j    -j   -j   -j   -j

In both cases the diagonal represents commutativity  
                                        
                                 ij = ji

and in this case the handedness term becomes 2yz and is added to or subtracted from the appropriate axis (or axes in case of non commutativity).

If David or somebody is prepared to run these transforms i would be interested to see the results.


I have designed a transform for the triplex ie ³ which is inspired by the transform on² and the notion of i being a transform in a set of transforms which include + - * / () and all algorithms. The syntax above the set imbues i with an additional property: that of a signal. Cardano when he first discussed these transforms used them as such. i will post the right handed transform later. There is of course a left handed transform which if the right handed one is interesting  i will derive from the construction process.

Will get back to using the unit vector multiplication method shortly, am just trying some alternatives closer to the Mandelbulb method.

Recently looked at Terry Gintz idynamasz as a more appropriate programme for this exploration.