Modeling cellular development using L-systems

Abstract

A fundamental process in nature is that of ontogeny, whereby a single mother cell—the zygote—gives rise, through successive divisions, to a complete multicellular organism. Over the years such developmental processes have been studied using different models, two of which shall be considered in this paper: L-systems and cellular automata. Each of these presents distinct advantages: L-systems are naturally suited to model growth processes, whereas if one wishes to consider physical aspects of the system, e.g., as pertaining to actual implementation in hardware, then an inherently spatial model is required—hence the cellular automaton. Our goals herein are: (1) to show how L-systems can be used to specify growing structures, and (2) to explore the relationship between L-systems and cellular automata. Specifically, we shall consider the case of membrane formation, whereby a grid of artificial molecules is divided into cells.