[wwalker3]

It's harder than you might think to model real physics with a cellular automaton.

Cellular automata are simulated on regular grids of cells, which gives them anisotropic (direction-dependent) behavior. For example, moving patterns in most automata can only travel in certain preferred directions (like gliders in Conway's game of life). And patterns that can move in multiple directions usually travel with different speeds in each direction.

In the real world, we don't observe any anisotropy in space, so none of the cellular automata I've seen proposed up to this point can model real physics, even in principle.

Lattice gas automata use hexagonal grids instead of square grids to alleviate this problem somewhat, but the anisotropy never really goes away, it's just reduced.

[maxharris]

NKS covers a lot more than just 1D or 2D cellular automata. See http://www.wolframscience.com/nksonline/section-5.5 and beyond.

[wwalker3]

You're right, NKS does cover more than cellular automata, like network systems (as your reference shows). But all the examples Wolfram gives of network systems have the same anisotropy problem as a cellular automaton. He uses mostly hexagonal grids for his network systems, which are better than square grids, but still not isotropic.

Wolfram doesn't give even a simple example of how two particle-like structures might repel or attract each other in an isotropic fashion in a network system (or any other system in NKS). That doesn't prove it's impossible, but if it is possible neither Wolfram nor anyone else seems to have any idea how to even get started.

[thisrod]

Can't you get rid of the grid, and connect the cells randomly? I have an notion that Feynman did that, but I don't remember where I heard about it.

[wwalker3]

That might very well fix the anisotropy problem (I haven't seen it done yet, but it sounds reasonable). However, that leaves you with another problem -- how do you create a stable particle-like pattern that can travel over a randomly-connected grid of connections without disintegrating :) Something like a Game of Life glider will explode if it hits a differently-connected area of the grid.

But say you solve that problem too -- there are many more problems after that. How do you encode the other properties of a particle like mass, charge, spin and momentum into this pattern? How can patterns attract and repel each other at long distances like real particles do?

These problems are probably all solvable, but my point to the original poster was that it's harder than it seems at first, and it's not something that's amenable to a simple search of the state space of possible automata.