2d equivalents of a 3d mandelbox?

[Mrz00m]

I've recently had nice results with concentric circles folded a square pattern, to emulate a drop falling in a square pond, except i made the drops bounce back to the centre from a square pond with variable size. The patterns are surprising variable, and they make me think of the mandelbox because the patterns are similar.

Is there a 2d mandelbox formula with a similar dergree of variation as teh 3d one, that can be zoomed in like a mandelbrot set? that would be cool because the patterns generated by squares and circles are extremely diverse even in just one iteration. it seems a cool avenue for research, circles folded onto squares. I know there are already some versions, could provide some web pages for them? if circles are folded over a square many times from different distances, the patterns could be interesting.

here is the waves emulator: <a href="http://www.youtube.com/v/hP4EwAPNVw0&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/hP4EwAPNVw0&rel=1&fs=1&hd=1</a>

[Mrz00m]

hey... i have this feeling some people could be thinking... " how do we break this gently mr zoom. No. you are in mathematical lalaland "   

[Tglad]

There is definitely some sort of similarity between a 2d Mandelbox and concentric rings bounced against a square box. This is because the box fold is a reflection around the box, which is exactly what a circular wave bouncing off a square box produces. The expansion of the wave is sort of represented by the scale factor in the Mandelbox equation.
However, it isn't exactly the same... a scale factor isn't the same as an enlargement of a ring by a fixed amount and the Mandelbox also includes a +C... but there is definitely similarity.

I think what your video is generating is standing waves... which is interesting in itself, of great interest to quantum theory for instance.

I agree with the general idea that invariant sets using the combination of linear and circular operations are interesting.

[laser blaster]

The mandelex is a 2D fractal that's very similar to the mandelbox (but not a direct analogue).

http://www.fractalforums.com/new-theories-and-research/an-interesting-fractal-the-mandelex-(inspired-by-the-box)/

[Mrz00m]

Thanks! very nice fractal and interesting, yes indeed, there are surely many possibilites with circles and cubes. i wrote a program for graphics shader to be able to see the standing wave emulator. here is the page, it needs a shader model 3 graphics card.
https://dl.dropboxusercontent.com/u/114667999/Public.html