Grammatical evolution to design fractal curves with a given dimension

摘要

Lindenmayer grammars have frequently been applied to represent fractal curves. In this work, the ideas behind grammar evolution are used to automatically generate and evolve Lindenmayer grammars which represent fractal curves with a fractal dimension that approximates a predefined required value. For many dimensions, this is a nontrivial task to be performed manually. The procedure we propose closely parallels biological evolution because it acts through three different levels: a genotype (a vector of integers), a protein-like intermediate level (the Lindenmayer grammar), and a phenotype (the fractal curve). Variation acts at the genotype level, while selection is performed at the phenotype level (by comparing the dimensions of the fractal curves to the desired value).