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

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