If you had to simulate such a universe in a computer program, how would you do it? What would it look like?

Perhaps instead of Brownian motion you'd have something more directed. Scientists inhabiting the universe would observe a "force" that brings elements of like kind together into nice orderly structures instead of random soups. It would be as if time ran in reverse. Perhaps instead of a big bang, the initial state would be a flat universe with just the minutest of perturbations in the energy gradient that would gradually evolve into a state of maximum order.