PROXIMAL ROOT DIAMETER AS PREDICTOR OF TOTAL ROOT SIZE FOR FRACTAL BRANCHING MODELS .2. NUMERICAL-MODEL

If root systems have scale-independent branching rules, the total number of links in the root system can be predicted from the ratio of the largest and smallest root diameter. In Paper I we presented an algebraic model for a dicho-syntomous pattern (the simplest form of proportionate branching forming two equal branches at each node) and a herringbone branching model (the simplest form of determinate branching rules). Here, we present a recursive computer model and its results to analyze intermediate patterns, derived from allotomous proportionate branching (with unequal branches). The numerical and algebraic model gave the same results when applied to the same situation and parameter values. For practical applications of the relations found, a test is required on whether or not the underlying assumptions are met. To illustrate such a test, measurements of the branching pattern were made on Mondriaan's Red Tree painting. For patterns such as this tree a slight dependency of the proportionality factor on root diameter and random variability of several parameters may have to be included.