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1-
p = 0.8; maxdepth = 6; 
1+
p = 0.9;
2-
tree[n, f] := (If[Length[Flatten[n]] > maxdepth, {}, 
2+
maxdepth = 4;
3-
   If[Or[RandomReal[] < p, Length[n] < 2], 
3+
tree[n_, f_] := (If[Length[Flatten[n]] > maxdepth, {}, 
4-
    Table[{n -> {n, i}, tree[{n, i}, f]}, {i, f}], {}]]); 
4+
    If[RandomReal[] < p, 
5-
tree[k_] := tree[{0}, k];
5+
     Table[{n -> {n, i}, tree[{n, i}, f]}, {i, f}], {}]]);
6-
t = tree[3]; GraphPlot[Flatten[t]]
6+
tree[k_] := 
7
  Map[FromDigits[Flatten@#[[1]], k] -> 
8
     FromDigits[Flatten@#[[2]], k] &, Flatten[tree[{0}, k]]];
9
t = tree[3];
10
GraphPlot[Flatten[t]]