priorFilter = Table[
   PDF[BetaBinomialDistribution[0.1, 0.9, 10]][x],
   {x, 0, 10}];
convolve[l_] := ListConvolve[priorFilter, l, {1, 1}, 0];
initial = Table[Boole[i == 1], {i, 100}];
initial /= Total[initial];
img = NestList[convolve, initial, 40];
Manipulate[
 ListLogPlot[img[[i]],
  PlotRange -> {{1, Length[img[[1]]]}, {0.0001, 1}}],
 {i, 1, Length[img], 1}
 ]