Expanding Aura

Kali

Fractal Supremo

Posts: 1138

Expanding Aura

« on: March 13, 2011, 06:28:55 PM »

Expanding Aura

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


« Last Edit: July 15, 2012, 08:44:00 PM by Kali »	Logged

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Fractal Ken

Fractal Lover

Posts: 246

Proud to be 2D

Re: Expanding Aura

« Reply #1 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.

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, 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 containing these sorts of pictures.


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Kali

Fractal Supremo

Posts: 1138

Re: Expanding Aura

« Reply #2 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, 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.


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Fractal Ken

Fractal Lover

Posts: 246

Proud to be 2D

Re: Expanding Aura

« Reply #3 on: March 14, 2011, 03:29:40 AM »

Quote from: Kali on March 14, 2011, 01:27:01 AM

Another thing that has me thinking, is a possible relation of the mandelbox with this patterns, 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.

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.


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it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval, thanks and see you perhaps in 10 years again

The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
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