A new favourite "Bulb"

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Offline FractalDave

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« on: September 13, 2018, 02:09:36 PM »
Hi all, I don't know how I overlooked this one....perhaps I just never checked the higher powers......it's actually fairly interesting as just ^2 or ^4 but I really like the ^8 version.

It's:

   r   i   j   k
r  r   i   j   k     
i  i  -r  -k   j
j  j  -k  -r   i
k k   j   i  -r

So (x,y,z,w)^2 = (x^2-y^2-z^2-w^2, 2xy+2zw, 2xz+2yw, 2xw-2yz

A quick render of the degree 8 straight from within UF is atached.
« Last Edit: September 13, 2018, 08:41:06 PM by FractalDave »
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Offline FractalDave

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« Reply #1 on: September 13, 2018, 04:59:38 PM »
BTW part of the reason I like this one is that the x-y and x-z 2D cross-sections of the x,y,z viewing space are exactly as they should be no matter whether you take z in (x,y,z,w) or w in (x,y,z,w) as the 3rd spatial dimension for rendering, the y-z cross-secton does change however -  something had to !!
Also the "bulbs" in each case are similar to those in the other but certainly not the same at any scale.

Another quick example below - not been fixed for a perfect render......