Can the universe be seen to have an information entropy close to zero? I recently made some thoughts about fractals and especially how much information they carry. If we consider for example the Mandelbrot set, we can basically "find" an infinite amount of patterns at different scales and sections but from an information theoretical point of view, such a chaotic and infinitely appearing construction should still carry very little information as any given point in the Mandelbrot set can be simply derived using the construction formula and a point's coordinate in the complex plane.
If we now assume that the universe also underlies some relatively simple formulae and constants (the theory of everything we haven't found yet), can it also be stated, that if this assumption holds, the universe as we know it also has an information entropy equal to the value of a maybe existing theory of everything, being close to zero or at least much lower to what it appears to be?
 A: The answer seems to me to be "yes", but not in an interesting way: it is possible, it is unlikely to be ruled out, but that also means it is not much of a physical theory. 
It would become physics if somebody proposed a very short TOE that made nontrivial predictions we could test and try to refine. Current work on this seems to me to be more metaphysics or math (e.g. Schmidthuber 2000) - fun, but not very constrained by observations.
The problem with very compact, low information TOEs is that they often generate "too much": it is not hard to make a theory that produces a vast multiverse and our world is well described by some tiny subset, but specifying which subset requires writing down a very specific "address" with many bits of information. (See Hutter 2010). Getting a short TOE that just produces us appears very hard. 
A: No. A theory of everything would not be expected to be a compact description of all the information in the universe. It would simply be a description of the time evolution of the universe.
