Towards universality of growth grammars: Models of Bell, Pages, and Takenaka revisited

Abstract

'Growth grammars' are extended parametric Lindenmayer systems, enriched by some novel features (expand operator, global sensitivity, interpretive rules, arithmetical-structural operators). They can serve as a formal basis for describing functional-structural plant models from the literature. This is demonstrated on three well-known models having in common that they were originally developed without using any formal grammars: an early, but quite general structural plant simulator by Bell, a root model by Pages and Kervella, and an above-ground tree model (involving competition for light) by Takenaka. The study considers the special extensions of L-systems necessary to rebuild some characteristic features of each of these models. The obtained degree of universality and the current limitations of the growth-grammar approach with respect to functional-structural tree models are discussed.