Grammatical evolution to design fractal curves with a given dimension

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  author =       "Alfonso Ortega and Abdel Latif {Abu Dalhoum} and 
                 Manuel Alfonseca",
  title =        "Grammatical evolution to design fractal curves with a
                 given dimension",
  journal =      "IBM Journal Research and Development",
  year =         "2003",
  volume =       "47",
  number =       "4",
  pages =        "483--493",
  month =        jul,
  keywords =     "genetic algorithms, genetic programming, grammatical
                 evolution, L-System",
  URL =          "",
  abstract =     "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
  notes =        "0018-8646/03/$5.00 deterministic grammar D0l. popsize

                 {"}Similar results could have been obtained by directly
                 apply GA to L-System{"} page 491. Genetic operations
                 include Fusion and Elision.",

Genetic Programming entries for Alfonso Ortega de la Puente Abdel Latif Abu Dalhoum Manuel Alfonseca