Two Geometrical Models of Branching of Botanical Trees

A botanical tree may be regarded as a system of axes which develop by repeated bifurcation. A complicated tree can be described by a few parameters of bifurcation which determine the geometry of the bifurcation process. A bifurcation model (H-model) has previously been proposed and shown to be useful for comparison with trees which have branch complexes which approach a horizontal plane (e.g. Terminalia). Another bifurcation model (P-model) is now proposed which is appropriate to branching systems in which successive branch planes are perpendicular to each other (e.g. Cameraria and Tabernaemontana of the Apocynaceae). By modification of the P-model to take into account a geotropic effect, a more realistic branching model for one kind of tree species is produced. The relationship among these geometrical models of branching is discussed and illustrated with computer simulations.