Here we animate how the self-contacting tree and its set of branch tips change with q . To make more clear the subtle changes around these critical points, the variable animations slow there. Other cases are more intricate. 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.
All pictures are the same absolute size, to illustrate the relative size of each of the trees.
The height of each picture is adjusted to the vertical extent of the tree. The aspect ratio is chosen to preserve slopes. All pictures are the same absolute size, to illustrate the relative size of each of the tip set. The height of each picture is adjusted to the vertical extent of the corresponding tree. The aspect ratio is chosen to preserve slopes.