Hi all,

I'm working on a model of self-organised critical systems following [B. Drossel and F. Schwabl, Physical Review Letters 69, 1629 (1992)] forest fire model to create a cellular automaton which counts the total number of fires within the lattice.

Given a matrix (100 x 100) with randomly generated integer values in range [0,2], on each timestep t, the matrix values will be updated according to 3 rules which change the values within the matrix, 0 -> 1 if rule1, 1 -> 2 if rule 2 etc. This would run over t time steps and then I would run the code "sample" number of times to create a pdf of the total count of each site.

I have attached the nb. Advice on increasing efficiency of the calculations is also more than welcome.

What I am trying to do next is create a dataset which notes the time taken for a 2 in the matrix to change back to a 2 after a series of rules has changed it cyclically from 2->0->1->2. Essentially looking at the wait times between the 2's occuring at a specific site.

To do this, I created a dataset:

wait = Dataset[{<|"run,i,j" -> {y, i, j}, "t" -> ii|>}];

Aiming to note which run of the code, where in the matrix the value 2 lies, and at what timestep it appears on. I would like to be able to append only the t values for a given value of {y, i , j} without duplication.

My first attempt to test these changes went like this:

n = 20;
sample = 4;
t = 10;
n = 20;
wait = Dataset[{<|"run,i,j" -> {y, i, j}, "t" -> ii|>}];
Nmat = Table[RandomInteger[{0, 1}], {n}, {n}];

For[y = 1, y < sample + 1, y++,

 For[ii = 1, ii < t + 1, ii++,

  For[i = 1, i < n + 1, i++,
    For[j = 1, j < n + 1, j++,

    If[Nmat[[i, j]] == 1,
     (*Add a value into the dataset noting the run and matrix \
component*)
     If[MemberQ[waittimes[[All, 1]], {y, i, j}],
      ]
     ]
    ]
   ]
  ]
 ]

However I get stuck on changing the values within the specifi row of the dataset. For example if a 2 occurs at "run,i,j" = {1,1,1} for t = 1 and then t = 5, I would like to append only the t column within the dataset where the specific row is {1,1,1}

Any help is more than welcome!