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This is just an idea I had, not a developed theory, but still could be of your interest.
(Also is not directly related to fractals -yet-, so I posted it here for now)

Let's take a set of spheres in space, and shrink them uniformally at a constant rate:

https://dl.dropbox.com/s/4x1ec45d4fc9iuh/shrink.swf

This is how it looks from the point of view of someone who is not shrinking, but what if the observer is also shrinking at the same rate?
(and any tool for measuring space that he could use)

In that case, the size of spheres will remain the same, but since the space between them is growing, the result will be:

https://dl.dropbox.com/s/v1hwond80z9j460/shrinkexpand.swf

So a shrinking observer on the surface of one sphere will see that other spheres are going away from each other, but will not notice the shrinking. Also if their size is decreasing (relatively to space) at a constant linear rate, guess what... the expansion will be an accelerated one, as you can see in the animation.
(I put the spheres arranged on a plane for not allowing the perspective view to make you think the spheres size are changing in the second animation)

So this is my question: Is the universe really expanding, or is the matter that is shrinking?

Again, is just an idea, a simple concept, I'm not claiming anything and I haven't developed a theory of the universe expansion based on this.
I just wanted to share it so you can tell me what you think, I'm open to any commentaries, critique and even laughs ;D

P.S.: I used Fragmentarium for the anims.

Very interesting.
I didn't think of it very deeply yet but *probably*, since all the laws of physics would shrink with that at an equal rate, this would not change anything on a physics level. Probably all the same laws as they are fleshed out right now, would behave in the very same way.

However, it's weird to think about it that way if you consider that there is a gap between all your atoms and such. Of course, some forces would hold them close to each other. A force would then be a gap-reducer. but by doing this you'd kinda detach yourself from yourself.

There is some inconsistency in this hypothesis. Contracting maps, i.e. functions that shrink a set of points, generally have attractors, subsets that map to itself under the mapping. In the simplest case, such an attractor is a fixed point, think center of gravity.

It seems to me that this particular hypothesis does not have consistent rules what the attractors are. Picking the centers of planets as fixed points is kind of arbitrary. When two planets are just touching each other, does each one have an attractive fixed point in its center, or do they both contract towards the point where they are touching?

This comment is not meant to discourage further exploration of the idea. Nothing starts out as perfect. I merely think that the key point behind this concept is not the shrinking, but the fixed points. Those are in need of good ideas. The shrinking is then the smaller part. (If the contracting map is continuous and smooth, then there will also be repellers and perhaps other subsets of special points. The initial simplicity might be deceiving.)

Thanks for the comments. Both gave me nice observations, I'll think about the points you mentioned, but consider I've used spheres here as abstract shapes for illustrating the concept, not intented to represent planets or something else, just to show the possibility of being fooled by our perceptions about what's really going on. I didn't think deeply -yet- on how to apply this to the real world. To do that I think I must start with the subatomic level, considering all the forces we know, and then how this should affect the larger structures... and this could be when fractals will be appearing on the show ;)

Btw, I did a search (http://search.yahoo.com/search;_ylt=ApXkPfEPG6ip_GRy3rScAe6GaLt_;_ylc=X1MDMjE0Mjk4ODQyMgRfcgMyBGZyA3lmcC10LTcyNQRuX2dwcwMwBG9yaWdpbgNhci55YWhvby5jb20EcXVlcnkDc2hyaW5raW5nIG1hdHRlcgRzYW8DMQ--?p=shrinking+matter&toggle=1&cop=mss&ei=UTF-8&fr=yfp-t-725) and I found this is not a new idea...