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Asked: 2026-05-23T16:43:04+00:00

In the book Modelling Cellular automata Simulations with mathematica , the author is using

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In the book Modelling Cellular automata Simulations with mathematica , the author is using the following code to simulate cellular automata in a two dimensional lattice,

From the Moore Neighbourhood the update rule is 

update[site, N, E, S, W, NE, SE, SW, NW]

where N =North, E= East , S=South, W=West, NE= North East, SE=South East, SW= South East, NW=North West. Those arguments represent the values of the nearest neigbours in the Moor Neighbourhood. To apply those rules it uses the code below,

Moore[func_, lat_]:= MapThread[func,Map[RotateRight[lat,#]&,
{{0,0},{1,0},{0,-1},{-1,0},{0,1},
{1,-1},{-1,-1},{-1,1},{1,1}}],2]

For a table like the following (page 144 from the book)

pasture= Table[Floor[Random[]+(preyDensity+predDensity)]*
Floor[1+Random[]+predDensity/(preyDensity+predDensity)],{n},{n}]/. 
2:>{RND,Random[Integer, {1,3}],Random[Integer,{1,5}]}

RND:= Random[Integer, {1,4}]

he is using the following update rule 

update[{_,0,0},_,_,_,_,_,_,_,_]  := {RND, 3,5}

My question is: By using a four dimensional table like the following? Can I also apply the following update rule?

InitialMatrix[x_, y_, age_, disease_] :=
  ReplacePart[
    Table[3, {x}, {y}, {age}, {disease}], {{_, _, 1, _} -> 
  0, {_, _, 2, 1} -> 
  Floor[dogpopulation*0.2/cellsno], {_, _, 2, 3} -> 
  Floor[dogpopulation*0.05/cellsno], {_, _, 3, 1} -> 
  Floor[dogpopulation*0.58/cellsno], {_, _, 3, 3} -> 
  Floor[dogpopulation*0.15/cellsno]}] /. 
  3 :> If[RandomReal[] > 0.2, 0, RandomInteger[{1, 2}]];


update[{{x_,0,0},{y_,z_,w_},{a_,b_,c_}},_,_,_,_,_,_,_,_] :=
                                            {{x-1,0,0},{y+z,0,w},{a,b,c}}

This is an example of how I think I can use my table to work with cellular automata. Can I do something like that? Or I am wrong?

Edit my table

By changing my table into the following code below can I use the update rule above?

MyMatrix[x_, y_, age_, disease_] :=
  Table[0, {x}, {y}] /. 
    0 :> ReplacePart[
      Table[3, {age}, {disease}], {{1, _} -> 0, {2, 1} -> 
    Floor[dogpopulation*0.2/cellsno], {2, 3} -> 
    Floor[dogpopulation*0.05/cellsno], {3, 1} -> 
    Floor[dogpopulation*0.58/cellsno], {3, 3} -> 
    Floor[dogpopulation*0.15/cellsno]}] /. 
   3 :> If[RandomReal[] > 0.2, 0, RandomInteger[{1, 2}]];
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1 Answer

  1. Editorial Team

    The book Modelling Cellular automata Simulations with mathematica was written more than 15 years ago, so would recommend looking at the CellularAutomaton[] function in Mathematica.

    The function CellularAutomaton[] is a little complex, but if you want to do 2D Moore CA this is how you call this function:

    CellualrAutomaton[{func[#]&,{},{1,1}},initialMatrixVal, numIterations];

    What the above code will do is call function func[], with the Moore neighborhood as fn param for each and every node in initialMatrixVal for “numIterations” times.

    The CellularAutomaton[] function assumes Periodic boundary conditions.

    Hope that helps!

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