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Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Borromean Julia
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Author Topic: Borromean Julia  (Read 774 times)
Description: Another example of ideological approach
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Furan
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« 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 smiley
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
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Furan
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« Reply #1 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.



A horizontal cross section. There are still some parts missing. The filled cores are unit circles.
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matsoljare
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« Reply #2 on: October 09, 2013, 07:03:34 PM »
Now can you make a fractal Klein bottle?
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Furan
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« Reply #3 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  wink
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« Reply #4 on: October 10, 2013, 11:40:33 AM »
Quote from: 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
    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.    cheesy
 

Quote from: 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  wink
If you do the Klein Bagel, will that come with Lox and cream cheese??     jabbering
 
« Last Edit: October 10, 2013, 01:27:45 PM by Nahee_Enterprises » Logged
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Furan
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« Reply #5 on: October 10, 2013, 01:20:06 PM »
I'll try an appropriate coloring function  wink
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Alef
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« Reply #6 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.
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fractal catalisator
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