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Update: Re: why my version does not work

Documentation >> ReplacePart:

• ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm 

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

• ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1] 

instead of using a For loop.

Original answer - updated:

ClearAll[aroundF, replaceF] aroundF[m_, t_] := Join @@ Function[{k}, DeleteDuplicates[Clip[#, {1, #2}] & @@@ Transpose[#] & /@ Thread[{k + # & /@ Tuples[{-1, 0, 1}, {2}], Dimensions[m]}, List, 1]]]/@ Position[m, t] replaceF[old_: 0, new_: 1][m_, t_] := MapAt[If[#===old, new, #] &, m, Join@@aroundF[m,t]] replaceF[][matrix0, -2] // TeXForm 

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

replaceF[0, aa][matrix0, -2] // TeXForm 

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $