Why do simple rules produce emergent behavior in Conway's Game of Life? [See video].

Drat! I had hoped to get back to this and add the link to Conway discussing the rules. Too late to edit, but it’s here.

Even one-dimensional cellular automata can show complex behavior. (I played with Conway’s “Life,” which is 2-dimensional, back in the 1970s.) Hard to say “why” but a lot of very smart people at the Santa Fe institute are working on it! Stephen Wolfram’s book is full of examples. It’s really surprising how simple rules govern complexity. It’s no wonder, then, that atoms can organize into stars & planets, and that biochemistry can organize into life—all spontaneously. I am confident that one day these deep mysteries will be understood. Perhaps there are underlying physical or mathematical laws not yet apparent to us. “Great Question.”

I’ve read about several cellular automata before.

First, I don’t think that it is a visualization of evolution on any level. Where are the competing species whose adaptations allow them to better survive and reproduce in a hostile environment?

But anyways, one better interpretation (in my opinion) is that of subatomic particles interacting. The terms used for these are gliders, oscillators, puffers, reflectors, still life, and many more.

For example a glider colliding with an eater (these actual terms sound informal) will annihilate the glider and leave the eager unharmed.

The very famous (as famous as cellular automata patterns can be) gosper glider gun can be described in terms of two large unstable particles being contained. The two largest particles are unstable and emit another smaller particle (a honeycomb) before reversing direction. On the outside, two blocks function to absorb those particles, since they would otherwise interact with and destroy the two larger particles. On the inside, the two honeycombs react with each other and create a glider.

@gasman Great book. Thanks for posting the link.

@PhiNotPi When you listen to what Conway says about it, you might conclude that life, the universe and everything are just higher level implementations of cellular automata.

@ETpro Well, if we are talking on cosmic scale, then it is possible for a very large version to effectively simulate organisms. The largest Game of Life simulation that people have ever run will be but the gluon holding together two quarks inside of a nucleus inside of an atom of the simulated universe.

The reason that I jumped the gun on saying “no” is that the vast majority of people that I have ever heard talk about Life tend to describe each cell of the board as a cell of an organism, which is a scale orders of magnitude different from the actual universe.

@PhiNotPi I completely agree that living cell and the cells on the Game of Life board are vastly different in complexity. More accurately, some like cellular automata is going on at the quantum level, and that’s what gives rise to emergent behavior like that of living cells.

@ETpro The book I linked to above, by Wolfram (the developer of the widely used software Mathematica), was criticized when it was published for being overly self-aggrandizing—starting with the title! At almost $30 it’s also pricey. I was lucky to find it at a used bookstore for only a buck or two. The cover art shows a one-dimensional cellular automaton—the cells are arrayed horizontally & generations proceed vertically.

@PhiNotPi Yes, cellular automata have no connection with biological cells. People also tend to confuse “nuclear” as it applies either to atoms or cells. Ignorance is alive & well as usual…

It’s intriguing to consider the quantization of space and time at the Planck scale as some sort of cosmic cellular automaton, but I haven’t seen much written about that, even from theorists. It might take centuries before we can know. Would make a good premise for a sci-fi story, however.

I’ve been thinking about the idea of the universe being a CA, and I think that there are a lot of obstacles that have not yet been discussed. All of the CA that I have seen always have two properties: there is a rigid grid, and there is a universal progression of time at the same rate. However, the effects of general relativity include warping space-time and time dilation. One big obstacle is the relativity of simultaneity, which no CA has.

Even though I doubt that the universe is a CA, it is possible for a CA to simulate our universe, becuase as far as I know the laws of physics and CAs are in the same category of Turing-completeness.

@PhiNotPi CAs can be established on any number of dimensions. So it is easy for me to conceive of them also being folded into themselves tightly. As to simultaneity, the Planck Unit basically defines the smallest measure of time that is possible, and though quite short, it is still a finite number. It just means that if quantum events proceed as cellular automata, they are able to react to adjacent cell conditions in very rapid succession. And it also means that simultaneity is perfectly possible—in fact essentially certain to emerge given a large enough number of cells.