Yeah I agree. There was a bit of discussion re conservation of energy here too. I do like thought experiments in cellular automata because of the spatially localized nature of the transition function, which matches our physics. Do you have any suggestions for automata that also have reversibility and conservation of energy?
That seems great. Is there any reason people talk a lot about Life instead of Critters?
(Seems like Critters also supports universal computers and many other kinds of machines. Are there any respects in which it is known to be less rich than Life?)
You’re probably right, but I can think of the following points.
Its rule is more complicated than Life’s, so its worse as an example of emergent complexity from simple rules (which was Conway’s original motivation).
It’s also a harder location to demonstrate self replication. Any self replicator in Critters would have to be fed with some food source.
I feel like they must exist (and there may not be that many simple nice ones). I expect someone who knows more physics could design them more easily.
My best guess would be to get both properties by defining the system via some kind of discrete hamiltonian. I don’t know how that works, i.e. if there is a way of making the hamiltonian discrete (in time and in values of the CA) that still gives you both properties and is generally nice. I would guess there is and that people have written papers about it. But it also seems like that could easily fail in one way or another.
It’s surprisingly non-trivial to find that by googling though I didn’t try very hard. May look a bit more tonight (or think about it a bit since it seems fun). Finding a suitable replacement for the game of life that has good conservation laws + reversibility (while still having a similar level of richness) would be nice.
I guess the important part of the hamiltonian construction may be just having the next state depend on x(t) and x(t-1) (apparently those are called second-order cellular automata). Once you do that it’s relatively easy to make them reversible, you just need the dependence of x(t+1) on x(t-1) to be a permutation. But I don’t know whether using finite differences for the hamiltonian will easily give you conservation of momentum + energy in the same way that it would with derivatives.
Yeah I agree. There was a bit of discussion re conservation of energy here too. I do like thought experiments in cellular automata because of the spatially localized nature of the transition function, which matches our physics. Do you have any suggestions for automata that also have reversibility and conservation of energy?
https://en.wikipedia.org/wiki/Critters_(cellular_automaton)
That seems great. Is there any reason people talk a lot about Life instead of Critters?
(Seems like Critters also supports universal computers and many other kinds of machines. Are there any respects in which it is known to be less rich than Life?)
You’re probably right, but I can think of the following points.
Its rule is more complicated than Life’s, so its worse as an example of emergent complexity from simple rules (which was Conway’s original motivation).
It’s also a harder location to demonstrate self replication. Any self replicator in Critters would have to be fed with some food source.
I feel like they must exist (and there may not be that many simple nice ones). I expect someone who knows more physics could design them more easily.
My best guess would be to get both properties by defining the system via some kind of discrete hamiltonian. I don’t know how that works, i.e. if there is a way of making the hamiltonian discrete (in time and in values of the CA) that still gives you both properties and is generally nice. I would guess there is and that people have written papers about it. But it also seems like that could easily fail in one way or another.
It’s surprisingly non-trivial to find that by googling though I didn’t try very hard. May look a bit more tonight (or think about it a bit since it seems fun). Finding a suitable replacement for the game of life that has good conservation laws + reversibility (while still having a similar level of richness) would be nice.
I guess the important part of the hamiltonian construction may be just having the next state depend on x(t) and x(t-1) (apparently those are called second-order cellular automata). Once you do that it’s relatively easy to make them reversible, you just need the dependence of x(t+1) on x(t-1) to be a permutation. But I don’t know whether using finite differences for the hamiltonian will easily give you conservation of momentum + energy in the same way that it would with derivatives.