Go easy, not an expert. My intuition tells me that the maximum possible entropy in a given space is going to coincide with the arrangement requiring the most information to describe it. Let me know if this is wrong. Ok, so now what I want to know is what an actual arrangement like this would look like physically if it could be realized. I want to know what it would look like if you blew it up so that the atoms were the size of marbles. Would it look random or would I see structure? Are there an infinite number of such arrangements? Do max entropy arrangements have certain characteristics or certain physical structures that they will always have? Are they required to be similar structurally in some way? A purely random arrangement doesn't seem right because you could get some areas that happen to be easier to describe than they could have been. I am getting the impression that it will resemble a fractal, but that doesn't sit right because a fractal repeats parts of itself and that makes a description easier. It seems like it would require small yet complex structures that don't repeat and don't contain versions of themselves, nor are contained within larger version of themselves. No repeats or copies or translations would be allowed. It's almost like the opposite of a fractal intuitively. It constantly does not repeat. But what does that look like? Anyone have any insight into this? [edited] Also, it seems like you would have to repeat certain structures if your area was large enough because you'd run out of possibilities. Then what does it look like?