Sorry for the incomplete information below, but my vocabulary not good
enough and my math neither but...

The real numbers along with addition and multiplication have very nice
properties (I think the word in english is "field", but not sure (too far in
my past)) and this the first dimension.

The complex numbers have the same property and this is 2nd dimension and
this is where Julias lie
(you know the formula : x(n+1) = x(n)*x(n) + a0))

Don't kook for 3rd dimension, it doesn't exist !

4th dimension is known as Quartenion (but we have to project them in the 3rd
dimension before ray-tracing), but we use the same formula (incidentaly
we've lost the property of commutativity at this stage !)

8th dimension is known as Octonion...

To fully undertand the multiplication (addition is straight forawrd) for
thoses different fields you have to know how the bases multiply each other,

Complex  : 1*i = i, 1*1 = 1, i*i = -1
Quarternion : 1*i = i...
                        i*j = k,  j*i = -k
                        j*k=i, k*j = -i
                        k*i=j, i*k = -j
                        i*i=j*j=k*k= -1

Octonion : same idea as in quaternion (I believe) that is e3*e4=e5 and other
permutations (not clear ?)

Philippe

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