# Dimensions of Fractal Trees

## Various Dimensions

There are three obvious fractals associated with these trees:

the set of branch tips, the canopy, and the shortest path.

The canopy is the set
of branch tips that can be reached by a path from far away without touching any other part of
the tree.

The shortest path is the path in the tree from the
branch tip (LR)^{infinity} to the branch tip (RL)^{infinity}.

The graph
below shows the dimesnion of the branch tips (top curve), the canopy (bottom curve),
and the shortest path (small circles).

Here is a sketch of the steps in deriving this graph. |

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