Fractal puzzle! (theory, not real)

[Kenneth]

Level1; take a sphear, cut it like a 2x2x2 and you got a twisty.

Next level; place a smaller sphear on top of the first level sphear in the six positions where the cuts meet in X's (the poles) and cut them in the same manner.

When twisting L1, ex: R the L2 hemisphears divided by the cut follows so half the U L2 sphear is now located on the B-face, Half F side is in U and so on.

At this point we are still in the real world, nothing odd happens but if we let all six L2 sphears rotate in the same manner as the L1 sphear then things are getting weird = fractal motion. The L2 at R-side would rotate R2 if we did R, the same happens to the four that follows the turn around while the last one on the L side only does an R just like the L1 (it does not rotate from following the L1 turn around, it is still in its original position).

Then we can add more, L3, L4 and so on!!

And/or more cuts, like 3x3x3 or 4x4x4....

I would love to see a puzzle like this made in computer animation but I won't do it myself

 

[Lotsofsloths]

Can you make a rough picture in paint or something?

 

[JBCM627]

Possibly like this? This is a fractal 2x2 I generated a while ago. Although all sides are the same colors. Or are you talking about one of the like menger sponges?

 

[Lucas Garron]

Cool idea. There're a lot of interesting things.
For example: Does anybody see a simple way to visual orbits? (How many orbits are there for spheres of a size?)


(Click for huge, or try medium.)
Also more cubical sub-cubes.

Can anyone think of a nice coloring that makes each sphere unique?

Animation would be a headache, but if enough people demand it, I can animate, like, an order-5 with random moves.
Also, should spheres be able to twist along a contact?

 

[Kenneth]

Animation can be done using recurrection in a tree structure.

I liked the "cubish" image, it was nice, for mere leves you need a zoom funtion to see the cases. But alredy 3 levels are many pices, probably hard enough

For colours, at least for a few levels, one can let the L2 on the blue side have normal colours but 33% blue in the White, red, green e.t.c., That follows so L3 has got 33% L2 face colour.

But if wee keep doing that for more levels the differences in colours for pices on the same level/side will be hard to distinguish.

 

[darkzelkova]

What program would you suggest for this? Apophysis? I could try to make it, but I doubt that I'd succeed xD

 

[Kenneth]

If I got it right a L5 will have a total of 12440 pices

8 * 6^4 + 8 * 6^3 + 8 * 6^2 + 8 * 6 + 8 (L1 has got 8, L2 6*8 and so on).



I think the most intresting thing is a L3 2x2 cut. But there is one thing with L3 and larger; the L3 pices will move into the L1 sphear. It is possible to remove all but the last level or the last two levels. Else it is not a big deal if some of the pices are inside the higer levels at some points, you can't make a real pussle like this and in anmiations everything is possible

Else a L2 3x3x3 is intresting, not many pices and much like our favorite puzzle.

Do an alg setting up a L1 case, solve it using a diffrent alg will affect only L2 and higher.