Borromean Julia

[Furan]

I'm still working on the basics, trying different parameters. There are still errors present, so stay tuned for updates
Size of ovals 4R x 2R
Julia C=0 power2 fractal on parameters r, phi[0...2pi] and theta[0...4R+2piR] with jumps between ovals.
input: X0 or Xn
find appropriate oval
find r, phi, theta
r <- r^2
phi <- 2*phi
theta <- 2*theta
evaluate position of theta (bend or straight section), calculate Xn+1
repeat for 5 cycles

[Furan]

As the formula doesn't represent a function but a tree of paths, I'm struggling with implementation. I'll probably choose the most potential path during iteration and then try all the others until one shows up stable. Or not. This approach might offer much tighter trifold knots too.



A horizontal cross section. There are still some parts missing. The filled cores are unit circles.

[matsoljare]

Now can you make a fractal Klein bottle?

[Furan]

The Klein Bagel could be interesting and easy to reproduce. I'm not sure about the bottle shape. That thing's gonna be ugly. I'll definitely try that. Thanks for the tip 

[Nahee_Enterprises]

   As the formula doesn't represent a function but a tree of paths, I'm struggling with implementation.
    I'll probably choose the most potential path during iteration and then try all the others until one shows up stable.
    Or not.   This approach might offer much tighter trifold knots too.
            http://furan.sweb.cz/Wall2013/BorromeanJulia400.jpg
    A horizontal cross section.   There are still some parts missing.   The filled cores are unit circles.
            http://furan.sweb.cz/Wall2013/CutPlane.jpg

Turned out fairly good!!  I find the cross-section very interesting.    
 

   The Klein Bagel could be interesting and easy to reproduce.   I'm not sure about the bottle shape.
    That thing's gonna be ugly.   I'll definitely try that.   Thanks for the tip  

If you do the Klein Bagel, will that come with Lox and cream cheese??    
 

[Furan]

I'll try an appropriate coloring function 

[Alef]

First one kind of lacks contrast but second one is pretty cool. Cooll shape.
Is this possible to show Poincaré conjecture? Animated or somehow, but maybe not, just a thought.