[corruption]

Question to those in the know: I've done a lot of data mining, statistics and inverse problems, but I've never even looked at cellular automata. Am I missing anything?

What are they used for - what problems can they solve that other methods can't?

[enneff]

"Am I missing anything?"

Not really. They're a fun diversion, and useful for some simulations, but that's about it.

[corruption]

So what's the big deal - why does Wolfram seem to think they are the answer to the world's problems? I'm confused - there must be something there, as he's obviously a smart guy.

[JoachimSchipper]

Wolfram has - correctly - noted that complexity can arise from simple systems (think Conway's Game of Life, but even simpler - Wolfram is into one-dimensional equivalents). This is, he says, akin to how many biological systems work (e.g. individual cells/neurons are pretty simple, but a human is very complex).

He also - correctly - observes that the explosion in computational power afforded by modern computers make certain scientific investigations possible that were previously infeasible (e.g. the proof of the four-colour theorem relying on exhaustively testing some 1800 possible scenarios, or numerical simulation of some very complex phenomena).

He then combines these two passions of his and asserts that therefore, computation based on simple systems gives insight into the secrets of life, the universe, and everything.

[corruption]

I can understand that position. If he's correct, it would seem like a small task to search the computational landscape and find automata that predict biological behavior or physics systems better than current models. Is this his approach? I don't see many (any?) papers like this in any of the fields I'm involved in - so has it been successful?

[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.

[JoachimSchipper]

That seems to be the approach he's advocating, yes. As to its success - well, you don't see many (any?) papers like this...

If you are interested in this, go read "Gödel Escher Bach". It brilliantly explores this complexity-from-simplicity theme and the consequences of various viewpoints. E.g. you can easily observe/guess whether someone likes to eat curry; however, deriving this from the atoms making up said person is utterly infeasible.

[jewbacca]

They're really simple, slight variations yield drastically different behaviour, and some setups are Turing-equivalent (given some liberties of interpretation). This is Wolfram's argument on why they would stand with the Riemann-Zeta function as most beloved to Alan Turing, if he'd only known about them.

More fundamentally underlying his advocacy is Wolfram's obsession with the things, which, 30 years on, has not yielded very much. They don't seem to be terribly useful. His wider investigation of the structure of computation is certainly worthwhile, but CAs, at least in the form Wolfram's written his bible about [1], don't seem to be the philosophical revelation he promoted them as.

[1] http://en.wikipedia.org/wiki/A_New_Kind_of_Science