Animations

Here we animate how the self-contacting tree and its set of branch tips change with q. All animations involve the angle range 10 degrees to 170 degrees, in 5 degree increments, except around the critical angles, 90 and 135 degrees, where smaller increments are taken. To make more clear the subtle changes around these critical points, the variable animations slow there. Note the 90 degree and 135 degree trees (and branch tips) are a filled-in rectangle and triangle. Other cases are more intricate. See Chapter 16 of [FGN] and [FT] for more details.

The fixed size animations run at constant speed, illustrating the dynamics of the branching geometry.

The variable size animations slow near the critical angles, aiding the examination of the topological phase transition at those angles.

The fixed tree animation (176K) shows the whole tree, through 10 levels of branching. All pictures are the same absolute size, to illustrate the relative size of each of the trees.

The variable tree animation (220K) shows the whole tree, through 10 levels of branching. The height of each picture is adjusted to the vertical extent of the tree. The aspect ratio is chosen to preserve slopes.

The fixed tip animation (132K) shows the branch tips, represented by the 13th level of branching. All pictures are the same absolute size, to illustrate the relative size of each of the tip set.

The variable tip animation (154K) shows the branch tips, represented by the 13th level of branching. The height of each picture is adjusted to the vertical extent of the corresponding tree. The aspect ratio is chosen to preserve slopes. Note an additional delay near the end, revealing a familiar shape.

Return to Introduction

Return to Definitions

Return to Self-contacting scaling

Continue to References