Title: Borromean Julia Post by: Furan on October 03, 2013, 07:05:38 AM 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 (http://furan.sweb.cz/Wall2013/BorromeanJulia960.jpg) Title: Re: Borromean Julia Post by: Furan on October 09, 2013, 10:47:55 AM 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) (http://furan.sweb.cz/Wall2013/BorromeanJulia1920.jpg) A horizontal cross section. There are still some parts missing. The filled cores are unit circles. (http://furan.sweb.cz/Wall2013/CutPlane.jpg) Title: Re: Borromean Julia Post by: matsoljare on October 09, 2013, 07:03:34 PM Now can you make a fractal Klein bottle?
Title: Re: Borromean Julia Post by: Furan on October 09, 2013, 07:23:17 PM 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 :dink:
Title: Re: Borromean Julia Post by: Nahee_Enterprises on October 10, 2013, 11:40:33 AM 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 (http://furan.sweb.cz/Wall2013/BorromeanJulia1920.jpg) A horizontal cross section. There are still some parts missing. The filled cores are unit circles. http://furan.sweb.cz/Wall2013/CutPlane.jpg (http://furan.sweb.cz/Wall2013/CutPlane.jpg) Turned out fairly good!! I find the cross-section very interesting. :D The Klein Bagel could be interesting and easy to reproduce. I'm not sure about the bottle shape. If you do the Klein Bagel, will that come with Lox and cream cheese?? :jabbering: That thing's gonna be ugly. I'll definitely try that. Thanks for the tip :dink: Title: Re: Borromean Julia Post by: Furan on October 10, 2013, 01:20:06 PM I'll try an appropriate coloring function :dink:
Title: Re: Borromean Julia Post by: Alef on October 10, 2013, 05:14:44 PM 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. |