Parallel Graph Grammars with Instantiation Rules Allow Efficient Structural Factorization of Virtual Vegetation

Abstract

Parallel rewriting of typed attributed graphs, based on the single-pushout approach extended by connection transformations, serves as the backbone of the multi-paradigm language XL, which is widely used in functional-structural plant modelling. XL allows to define instantiation rules, which enable an instancing of graphs at runtime for frequently occurring substructures, e.g., in 3-d models of botanical trees. This helps to save computer memory during complex simulations of vegetation structure. Instantiation rules can be called recursively and with references to graph nodes, thus providing a unifying formal framework for various concepts from the literature: object instancing, structural factorization, Xfrog multiplier nodes, L-systems with interpretation. We give simple examples and measure the computation time for an idealized growing virtual plant, taken from the GreenLab model, in its implementation with instantiation rules in XL, compared to a version without instantiation rules.