Expanding Aura

[Kali]

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

[Fractal Ken]

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.

[Kali]

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.

[Fractal Ken]

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.