Growth models (including terminal and segmental branching) for topological binary trees.

A growth model for topological trees is formulated as a generalization of the terminal and segmental growth model. For this parameterized growth model, expressions are derived for the partition probabilities (probabilities of subtree pairs of certain degrees). The probabilities of complete trees are easily derived from these partition probabilities. 1. Introduction. In the study of growth of branching patterns much attention has been paid to the so-called terminal and segmental growth models. These models differ in that segmental growth allows all segments to branch with .equal probability, whereas terminal growth allows only terminal segments to branch with equal probability. In the field of neuroscience, where dendritic structures are frequently studied, the terminal growth model has often appeared to give a good fit to the experimental data (e.g. deviations from the terminal model are also reported under normal growth conditions (e. have calculated the probabilities of small two dimensional (2-D) stream channel networks for three growth models, viz: terminal growth, segmental growth and a model with fixed unequal non-zero branching probabilities for intermediate and terminal segments. The probabilities of these networks were obtained by enumerating all possible growth paths. They found that terminal growth did not fit any data set but that both other models were able to fit almost all the data. These examples show that (1) the terminal and segmental growth models are often able to describe experimental data, but also that (2) in many cases a better fit with the data should be expected if the branching probabilities of intermediate and terminal segments could be varied continuously. For this purpose, a growth model has been formulated mathematically which is provided with a parameter describing the ratio of branching probabilities of intermediate and terminal segments. For two particular