Tim Wegner wrote:
The correct formula is:
Then q1q2 = 1(x1x2 - y1y2 - z1z2 - w1w2) + i(y1x2 + x1y2 - w1z2 + z1w2) + j(z1x2 + w1y2 + x1z2 - y1w2) + k(w1x2 - z1y2 + y1z2 + x1w2)
Provided one knows the formula for complex multiplication by heart (and which fractal geek doesn't :^)), then it's easier to put the four elements of a quaternion into two complex variables and go from there: q1 = (a1,b1), where a1 = x1 + i*y1 and b1 = z1 + i*w1 q2 = (a2,b2), where a2 = x2 + i*y2 and b2 = z2 + i*w2 q3 = q1*q2 --> a3 = a1*a2 - b1*conj(b2) b3 = a1*b2 + b1*conj(a2) Except for the two conjugations this multiplication has an identical look to the one for complex numbers (the latter done in real numbers, of course). And that form is very convenient when using quaternions in Fractint's formula parser... Regards, Gerald