The exact probabilities of branching patterns under terminal and segmental growth hypotheses

Information about the way of branching of dendritic arborizations may be obtained by comparing the frequency distributions of observed branching patterns with theoretical distributions based on well-defined growth models. Two models usually get much attention in geomorphological and (neuro)biological studies, viz. terminal growth and segmental growth. Formulae to construct the exact probability distributions for both growth models are presented. It is shown that ranking and lumping of the individual branching patterns enable the analysis of very large arborizations with relatively few data. The application of the Kolmogorov goodness-of-fit test for discrete distributions to the analysis is discussed.