Cellular Automata update rules Mathematica

I am trying to built some rules about cellular automata. In every cell I开发者_JAVA技巧 don't have one element (predator/prey) I have a number of population. To achieve movement between my population can I compare every cell with one of its neighbours every time? or do I have to compare the cell with all of its neighbours and add some conditions.

I am using Moore neighbourhood with the following update function

update[site,_,_,_,_,_,_,_,_]

I tried to make them move according to all of their neighbours but it's very complicated and I am wondering if by simplify it and check it with all of its neighbours individually it will be wrong.

Thanks

As a general advice I would recommend against going down the pattern recognition technique in Mathematica for specifying the rule table in CA, they tend to get out of hand very quickly.

Doing a predator-prey kind of simulation with CA is a little tricky since in each step, (unlike in traditional CA) the value of the center cell changes ALONG WITH THE VALUE OF THE NEIGHBOR CELL!

This will lead to issues since when the transition function is applied on the neighbor cell it will again compute a new value for itself, but it also needs to "remember" the changes done to it previously when it was a neighbor.

In fluid dynamics simulations using CA, they encounter problems like this and they use a different neighborhood called Margolus neighborhood. In a Margolus neighborhood, the CA lattice is broken into distinct blocks and the update rule applied on each block. In the next step the block boundaries are changed and the transition rules applied on the new boundary, hence information transfer occurs across block boundaries.

Before I give my best attempted answer, you have to realize that your question is oddly phrased. The update rules of your cellular automaton are specified by you, so I wouldn't know whether you have additional conditions you need to implement.

I think you're asking what is the best way to select a neighborhood, and you can do this with Part:

(* We abbreviate 'nbhd' for neighborhood *)

getNbhd[A_, i_Integer?Positive, j_Integer?Positive] := 
    A[[i - 1 ;; i + 1, j - 1 ;; j + 1]];

This will select the appropriate Moore neighborhood, including the additional central cell, which you can filter out when you call your update function.

Specifically, to perform the update step of a cellular automaton, one must update all cells simultaneously. In the real world, this means creating a separate array, and placing the updated values there, scrapping the original array afterward.

For more details, see my blog post on Cellular Automata, which includes an implementation of Conway's Game of Life in Mathematica.