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Simultaneous Evolution of Bracketed L-system Rules and Interpretation

An L-system or Lindenmayer system consists of a grammar together with an interpreter. The grammar contains an axiom string and rules which are expanded into a longer string. The interpreter then renders the string into an object. The first use of L-systems was to provide morphological models of plants. In this study an evolutionary algorithm is used to perform selection on both the L-system grammar and interpreter parameters. The grammar is encoded in a set of real parameters that also includes the interpreter control parameters. This permits the evolutionary algorithm to acts solely as a real parameter optimizer. The interpreter is a graphic turtle with a stack. The evolutionary algorithm co-evolves the grammar and the turtle's control parameters to cause it to place a virtual plant in a constrained area of the Cartesian plane. Compared to previous studies in which the grammar was left fixed, the simultaneous evolution of grammar and interpretation parameters produces a richer selection of virtual plants. The L-system selection algorithm presented here is a potentially valuable tool for digital artists or virtual environment designers.