An excellent discussion of combinatorics. I have a physics theory that is based on the idea that the universe is actually expanding at the velocity we call the speed of light. This expansion drives the motion of matter, which is of 1, 2 or 3 rotational vectors, which affects their motion relative to their original position in the 'grid' when they first arise. Electrons push around inert particles like Protons and Neutrons and so forth. Photons push around electrons. They have different interactions with each other. If you assume the idea that electrons are pushing matter together at the speed of light, then you see that the space can be expanding, the source of energy becomes visible, and the mechanism of gravity starts with the activity of electrons - mostly the ones you can't see because they are massive in number and disordered, except for this tendency to cluster around other matter and push it together (anisotropy).

Naturally, my hypothesis shows absolutely mind-boggling sizes of numbers, and worse, they are doubling at a rate that the expansion edge of any given dot within the system is the speed of light in every direction radiating out. I find it very difficult to really fully explain the model to people. It's something related to the Electric Universe theory, but my first assumption, that Space is expanding, is not. The model I have also explain Dark Matter and Dark Energy, and the Red Shift. It also implies that although the universe is finite at any given moment, it is always expanding. Picture this Library of Babel, except every femtosecond every book gets 1 letter longer, and the number of books has to expand to accommodate the possibilities.

What I think is beautiful about this metaphor is the idea that the universe is simply an information system, an unfolding fractal in which the means to ponder upon what it even is can itself arise in the patterns that come out of it. I think a lot of people are repulsed by the idea that they are nothing more than machines, or perhaps more accurately, kinds of computers, but I think if you accommodate my model described above in this comment, you realise that the fluidity and complexity of this system literally can only get more and more intense, more and more vast, more and more interesting and, literally, eternally grow.

If God is the sum of all, at the end of the endless time, then there is even room for God in all of this. But like infinity, it is something that never fully can be seen here in the moment, any moment, at any time.