[qubex]

Obviously the minimum possible amount of data for a “Game of Life”-type setup would be a bunch of ‘ON’ voxels somewhere near the center.

As for the question itself, I think you’ve answered yourself: a Game of Life-type setup defined in three dimensions. I’ve seen a mention on HN of somebody implementing the (2D standard case) in 23 assembler instructions, so it’s very minimal.

[Someone]

Nitpick: 23 assembly instructions and billions of transistors to run them. Custom hardware for the game of life could significantly decrease that (and the number of instructions), though.

I also think that “bunch of ‘ON’ pixels” would have to be rather large, if you think the universe could have evolved in many, many, different ways. A stochastic version of the game of life might be a better choice.

To prevent that from getting to chaotic, the next state of a cell could depend not only on the states of neighboring cells, but also on the past state(s) of the cell and its neighbors (in a sense making ‘time’ more important). Alternatively, one could slowly decrease the amount of randomness over time, allowing the universe to ‘cool down’ from an initial Big Bang into a less chaotic almost stable state.

Finding an interesting variant would be a challenge, though.

[qubex]

I think Stephen Wolfram would beg to differ with you on the topic of how difficult it is to find an ‘interesting la rule – his hole oeuvre (whatever your opinion of the man) demonstrates that these things crop up surprisingly often with even the basest ingredients.

With regards to the kind of rule you speak of, a cellular automata cell in a 3D environment has at most 26 neighbours in the lattice. You could easily increment that to 27 if you wish to make its behaviour depend on its prior state (or even 53 if it you want it to depend on its 26 neighbours’ current state plus 27 prior states of itself and its neighbours). I built such systems (albeit on dynamic networks and 2D automata lattices) for my thesis nigh on 18 years ago. It’s quite utterly trivial.

[calmchaos]

Yeah. The reason this is interesting is that although our known universe seems very complex and chaotic, on (sub)quantum level the core rules are extremely simple, always followed and there aren't that many of them.

Designing a three dimensional system is a lot harder than a simple Game of Life though.

[qubex]

Funnily enough I would have said the exact same thing for exactly opposite reasons: on our level everything looks very regular despite the underlying subatomic world being totally nondeterministic.