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Insect Fractal

Ok everyone knows the mandlebrot set fractal

Zn+1 = Zn^2 + C

I was playing around with that formula, but tried to do a 3D form of it, so I created a 3-component complex number. Defining addition and subtraction for that is easy enough but multiplication is just wtf, so I defined it as so:

(a,b,c)*(d,e,f) = (a*a-b*b-c*c, (a+b)*(d+e)-a*a-b*b-c*c, (b+c)*(e+f)-b*b-c*c)

Just basically some random typing.

C is initialized to (x, y, z)

This is the slice at z = -.5

I don't know what else to call this fractal, but I think it looks like an insect.

It is impossible to fully define a 3 component complex number unfortunately. Looks great!

Huh, would be interesting to see the results of other z values. I can see where you got the insect idea from, maybe you can find other fractimals in this set fractal (Uncontrollable excitement)!

Since I know next to nothing about fractals, is this "shape" infinite? could you slap in any finite z value and come up with something?

Really cool and everything...

But please don't make my head hurt with the fucking description. Looks a bit like a rat to me

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Nov 16, 2009
10:59 PM EST
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