# Dimensions of Fractal Trees

## Self-Contacting Trees

In the tree pictured above the branch tip marked * can
be reached in two ways

LRRRRLRLRLRLRLR... =
LR^{4}(LR)^{infinity}

and

RLLLLRLRLRLRLRL... =
RL^{4}(RL)^{infinity}

Consequently, for both sequences, the corresponding branch
tips have x-coordinate 0.

With simple trigonometry these sequences are converted into geometric series,
giving r as a function of q. |

Here is a graph of the self-contacting r as
a function of q. |

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