Growing biological systems can be described as dynamical systems with a dynamical structure. In such systems not only the values of variables characterizing system components, but also the number of components and the connections between them, may change over time. For example, in a developing plant, the numbers of branches, leaves and flowers change as the plant grows, and the topology and form of the plant are gradually modified. A simulation model of a plant must therefore be capable of dealing with the changing numbers of components, and their varying configurations. This problem was explicitly addressed by Lindenmayer, who introduced L-systems as a formalism for modeling structures with a dynamically changing topology. This formalism, extended with a geometric interpretation, has subsequently been applied to model a wide variety of plants.
The modeling of developing surface structures has recently been addressed from new viewpoints by Giavitto and Michel (the MGS system), and Smith et al. (the vv system). Here we outline this latter approach and its potential applications to the modeling of biological structures.
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