Mutating tree

(* init with this:*)
Needs["MultivariateStatistics`"];
anim = {};
mut = 0;
n = 3;
Clear[line]; Clear[tree];
line[1, i_] :=
  line[1, i] = Accumulate[Join[{{0, 0}}, Table[{1, 0}, {10}]]];
line[n_, i_] :=
  line[n, i] =
   SortBy[line[n - 1, i] +
     Join[{{0, 0}},
      RandomReal[NormalDistribution[0, 0.1], {10, 2}]], #[[1]] &];
tree[i_] :=
  tree[i] =
   Table[Map[RotationMatrix[0.3 (k - (n + 1)/2)].# &,
     Join[{{0, 0}}, MovingAverage[line[i, k], 2]]], {k, 3}];

(* then run this a few times:*)
Cl[n_, rot_, pos_, s_] :=
  ListLinePlot[
   Map[RotationMatrix[rot].(# s) + pos &,
    tree[mut max - mut n + 1], {2}], Joined -> True,
   InterpolationOrder -> 2, PlotRange -> All, AspectRatio -> 1,
   Axes -> None, PlotStyle -> Black];
Crec[0, pos_, s_, rot_] = {Graphics[]};
Crec[n_, pos_, s_, rot_] :=
  Module[{endpoints = Map[Last, tree[mut max - mut n + 1]]},
   Join[{Cl[n, rot, pos, s]},
    Crec[n - 1, pos + s RotationMatrix[rot].endpoints[[1]], s/3,
     rot - 0.3],
    Crec[n - 1, pos + s RotationMatrix[rot].endpoints[[2]], s/3, rot],
    Crec[n - 1, pos + s RotationMatrix[rot].endpoints[[3]], s/3,
     rot + 0.3]]
   ];
max = 5;
c = Show[Crec[max, {0, 0}, 1, 0], ImageSize -> {300}];
anim = Append[anim, c];
mut += 1;

(* then export: *)

Export["treemut.gif", Join[anim, Reverse@anim]];