17
Oct
04

### Tree Fractal

Tree Fractal – adapted from from Renan Cabrera’s Mathematica code. This is an example of a bracketed Lindenmayer System (L-System). You can also use this technique to make lightning bolts.
```(* runtime: 1 second *) Polar[{x_, y_}, theta_, r_] := {x + r Cos[theta], y + r Sin[theta]}; branch[x_] := x; branch[tree_List] := branch /@ tree; branch[Line[{p1_, p2_}]] := Module[{r = Sqrt[(p2[[1]] - p1[[1]])^2 + (p2[[2]] - p1[[2]])^2], theta = ArcTan[p2[[1]] - p1[[1]], p2[[2]] - p1[[2]]]}, {Thickness[0.05r], RGBColor[0.5r, 1 - 0.75r, 0], Line[{p2, Polar[p2, theta - Pi/6, 0.8r]}], Line[{p2, Polar[p2, theta + Pi/4, 0.7r]}]}]; Show[Graphics[{Thickness[0.07], RGBColor[0.5, 0.25, 0], NestList[branch, Line[{{0, 0}, {0, 1}}], 12]}], AspectRatio -> 1, Background -> RGBColor[0, 0, 0], PlotRange -> {{-3, 3}, {0, 6}}];```

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