A General Random Combinatorial Model of Botanical Trees

We present a new mathematical model of botanical trees capable of simulating the combinatorial structure of specific species based on their bifurcation ratios. We first describe a general combinatorial model of botanical trees for the purpose of synthetic imagery. We apply techniques from probabilistic analysis to generate random combinatorial trees and then model them as three-dimensional geometric trees. We choose modelling functions that are partially based on results from theoretical biology. By changing the underlying distribution used to generate the random combinatorial trees, we are able to produce images of a wide variety of botanical trees. For example, just one parameter controls the branching from dichotomous to monopodial. We then parameterize the model acording to Hortonʹs first law. We implement our algorithm in L-systems, a popular botanical modelling language.