A fractal has an axis of scale symmetry - "move about", ie: move up and down in scale, and the world remains the same.
See for example coastlines and menger sponges
Even in a universe...
But Rade this is just holding a mirror to one scale - how you imagine the very small Planck scale to be. So of course you see a simple reflection symmetry.
There is also the second possible axis of symmety, the asymmetric one that is local~global or fractal in nature.
Seems to me you have in mind questions of conservation laws and entropy - why is the creation of more void, an expanding universe, allowed? Why does the universe expand in short.
The "points" of the universe are Planck-scale. You could also ask why they don't expand as the Universe grows...
Take your point but it is probably right to say that the vacuum would be the lowest possible state of the system, the natural end state. Give the universe enough time and all those pesky matter/gravity bumps will be flattened out - dissipated - to make a flat spacetime void.
You raise a number of points that we will be forbidden to discuss as they will be deemed "not physics".
So I only offer quick replies.
Salthe is a theoretical biologist, but has developed a mathematically general framework that can apply to any kind of system.
google on Stan Salthe but I think his stuff on the web mostly concerns his "specification" hierarchy rather than his "scalar" hierarchy. It is in his 1985 book evolving hierarchical systems.
I would explain but the posts would get censorsed as "not physics".
Nice question. I would expect the conventional answer is that space - being homogenous and isotropic - would be self-dual. The reflection would be the same.
This would be a reflection of space at the same scale - across the axis of symmetry.
But there may be also the axis of asymmetry -...
Still seems crazy that you would pick on that of all things to "correct". There is endless other stuff I write that could do with actual correction.
Anyway, in that post I was flagging the FRACTAL sphere packing story in a perhaps too subtle hint that people should consider instead a dynamic...
Would it have helped to have said that there are two regular ways of stacking? But, of course, you could mix the binary choice made with each layer to generate an infinity of "different" outcomes?
If that is all you are saying here, it seems a puzzlingly pedantic point. And is neither here...
Hi Josh - why is it ugly?
There seem two alternative views on the landscape.
1) The first is that it is a set of crisp probabilities. That is, every possible solution actually has existence and we happen anthropically to be in one outcome in which existence can be reported.
Whoops! You are quite right. The visible Universe is flat (which implies it is at the critical density) and the rate of expansion is a separate issue to the geometry.
The old story was that the rate was decelerating due to gravity acting on mass - the coasting to a halt scenario. The new...
Yes, there are three alternatives. You can have flat space (which coasts to a halt at infinity), closed space (that will collapse) or openly expanding space (which has hyperbolic curvature and accelerates away).
The recent fuss about dark energy, quintessence or cosmological constant is due...