agent-based models vs. CAs
Here is my attempt to better articulate my argument that agent-based models are representable as CAs (which we already know because a Turing machine can be built in Conway's life... but this shows that it's not very complicated to do for a simple agent-based model like Langton's Ant): (also, before the argument, the implication I'm going for--that the distinction between CAs and agent-based models is in fact arbitrary, and although this does not mean that the distinction is not a useful concept, we should recognize its subjectivity) I think that any agent-based model can be represented as a CA. Granted, the rules will have to be more complex, but it is still entirely possible to rewrite agents and their environments as elements of a single CA. For example, Langton's Ant: (and this is just one of several ways to do it--the added complexity can be represented differently in the rules) can be rewritten as a 2D CA in which each cell has 4 states: on, off, on + Ant, off + Ant. Really this is just two booleans variables per cell instead of the one we are used to. The rules are: A cell maintains its state unless a neighboring cell's ant state is on and the ant is "facing" that cell, in which case that cell's ant state is turned on and it's color switched. The issue of the direction the ant is facing could be dealt with by giving each cell a 4-valued variable (valued up, down, left, or right) and setting all of these initially to whatever direction the ant starts out facing (up). The values change as a function of what direction value the cell that previously "was the ant" had. Clearly, the same rules are applied at each iteration to every cell in this system and to nothing but the cells (no agent), and it gives rise to the exact same behavior as Langton's ant. I challenge anyone to find an "agent" in this CA. There is no agent because there is no encapsulated information that is specially treated. Of course, it is more efficient (and easier to understand, probably) to write this system as an agent-based model, but maybe this example can serve as a reminder that there is nothing that agent-based models can do that CAs can't. A more direct and complete proof of this is the fact that a Turing machine can be built in Conway's life.