Title: Expanding Aura Post by: Kali on March 13, 2011, 06:28:55 PM Expanding Aura
(http://nocache-nocookies.digitalgott.com/gallery/6/3869_13_03_11_6_28_55.jpeg) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6107 Selfmade Mandelbox-like 2D formula: x=x-(x-trunc(x))*2 y=y-(y-trunc(y))*2 m=x*x+y*y x=x/m y=y/m "Exponential smoothing" inside coloring formula from UF5 Title: Re: Expanding Aura Post by: Fractal Ken on March 13, 2011, 07:57:40 PM The nested circles produce a really nice effect!
Using totally different methods, I made a fractal two years ago which I titled Aura. (http://i1122.photobucket.com/albums/l540/Fractal_Ken/aura.png) I like how you're modifying the mandelbox approach. Here's an additional idea I've been exploring: Treat the 2D mandelbox vector as a complex variable. For example, using Tglad's notation (http://sites.google.com/site/mandelbox/what-is-a-mandelbox), I write formulas like v = s*[ballFold(r, f*boxFold(v))]^2 + c The idea is that the modified v has two components, so we can pretend it's a complex number and perform any complex arithmetic operation on it. I've started a gallery (http://www.fractalforums.com/index.php?action=gallery;su=user;cat=342;u=3752) containing these sorts of pictures. Title: Re: Expanding Aura Post by: Kali on March 14, 2011, 01:27:01 AM Interesting pic, Ken... and another coincidence! :)
I like the idea of using complex numbers with the folds. I already saw the images in your gallery, but didn't know they were generated that way. BTW, I liked the tic-tac-toe a lot :) I'll give it a try and see what happens with complex numbers and my linear folding method. Another thing that has me thinking, is a possible relation of the mandelbox with this patterns (http://www.fractalforums.com/general-discussion-b77/fractal-patterns-from-decimal-extraction/msg28216/#msg28216), remember? I'm not ready to fully describe my idea yet, but in short terms: I think there's also a square vs. circle relation in the patterns I discovered, just like the box & ball fold of the Mandelbox. Title: Re: Expanding Aura Post by: Fractal Ken on March 14, 2011, 03:29:40 AM Another thing that has me thinking, is a possible relation of the mandelbox with this patterns (http://www.fractalforums.com/general-discussion-b77/fractal-patterns-from-decimal-extraction/msg28216/#msg28216), remember? Offhand, the relationship isn't evident to me, but I'm probably just being dense. :) I'll be interested to see what you come up with.I'm not ready to fully describe my idea yet, but in short terms: I think there's also a square vs. circle relation in the patterns I discovered, just like the box & ball fold of the Mandelbox. |