Dimensions of Fractal Trees

Self-Contacting Trees

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

LRRRRLRLRLRLRLR... = LR⁴(LR)^infinity

and

RLLLLRLRLRLRLRL... = RL⁴(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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