A tree is called *self-contacting* if the tips of some left branches
coincide with the tips of some right branches, but no tip coincides with
any non-tip point of the tree. For each value of q, exactly one value of *r* scales the
branches to self-contact. This graph shows that *r* as a function of
q.
See [FT] for a derivation of this graph.

The angles *critical angles*: here both the tree and the set of branch tips form
a filled-in rectangle (*topological phase
transition*. These phase transitions are illustrated by the variable tree and variable tip animations.

Return to Introduction

Return to Definitions

Continue to Animations

Continue to References