Inferring Temporal Parametric L-systems Using Cartesian Genetic Programming

Lindenmayer Systems (L-systems) are formal grammars that use rewriting rules to replace, in parallel, every symbol in a string with a replacement string. By iterating, a sequence of strings is produced whose symbols can model temporal processes by interpreting them as simulation instructions. Among the types of L-systems, parametric L-systems are considered useful for simulating mechanisms that change based on different influences as the parameters change. Typically, L-systems are found by taking precise measurements and using existing knowledge, which can be addressed by automatic inference. This paper presents the Plant Model Inference Tool for Parametric L-systems (PMIT-PARAM) that can automatically learn parametric L-systems from a sequence of strings generated, where at least one parameter represents time. PMIT-PARAM is evaluated on a test suite of 20 known parametric L-systems, and is found to be able to infer the correct rewriting rules for the 18 L-systems containing only non-erasing productions; however, it can find appropriate parametric equations for all 20 of the L-systems. Inferring L-systems algorithmically not only can automatically learn models and simulations of a process with potentially less effort than doing so by hand, but it may also help reveal the scientific principles governing how the process' mechanisms change over time.