Grammatical evolution to design fractal curves with a given dimension

Original paper in http://ieeexplore.ieee.org/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).This paper has been sponsored by the Spanish Ministry of Science and Technology (MCYT), project numbers TIC2002-01948 and TIC2001-0685-C02-01

Computer-Generated music using grammatical evolution

This is an electronic version of the paper presented at the Middle Eastern Simulation Multiconference (MESM) held in Amman (Jordan) on 2008This paper proposes a new musical notation with Lindenmayer grammars, and describes the use of grammar evolution for the automatic generation of music expressed in this notation, with the normalized compression distance as the fitness function. The computer music generated tries to reproduce the style of a selected pre-existent piece of music. In spite of the simplicity of the algorithm, the procedure obtains interesting results.This work has been partially sponsored by the Spanish Ministry of Science and Technology (MCYT), project number TIC2002-01948

Grammatical Evolution with Restarts for Fast Fractal Generation

In a previous work, the authors proposed a Grammatical Evolution algorithm to automatically generate Lindenmayer Systems which represent fractal curves with a pre-determined fractal dimension. This paper gives strong statistical evidence that the probability distributions of the execution time of that algorithm exhibits a heavy tail with an hyperbolic probability decay for long executions, which explains the erratic performance of different executions of the algorithm. Three different restart strategies have been incorporated in the algorithm to mitigate the problems associated to heavy tail distributions: the first assumes full knowledge of the execution time probability distribution, the second and third assume no knowledge. These strategies exploit the fact that the probability of finding a solution in short executions is non-negligible and yield a severe reduction, both in the expected execution time (up to one order of magnitude) and in its variance, which is reduced from an infinite to a finite value.Comment: 26 pages, 13 figures, Extended version of the paper presented at ANNIE'0

Optimizing ecology-friendly drawing of plans of buildings by means of grammatical evolution

This is an electronic version of the paper presented at the International Industrial Simulation Conference (ISC 2006), held in Palermo (Italy)We explore the application of grammatical evolution to the automatic generation of plans of building with constraints. A BNF is presented that guarantees the conversion of the genetic code into a well formed geometrical figure or phenotype. The validity of the approach is demonstrated, its limitations are analyzed and new evolutionary techniques are suggested for future work in this area

Global distributed evolution of L-systems fractals

Internet based parallel genetic programming (GP) creates fractal patterns like Koch’s snow flake. Pfeiffer, http://www.cs.ucl.ac.uk/staff/W.Langdon/pfeiffer.html, by analogy with seed/embryo development, uses Lindenmayer grammars and LOGO style turtle graphics written in Javascript and Perl. 298 novel pictures were produced. Images are placed in animated snow globes (computerised snowstorms) by www web browsers anywhere on the planet. We discuss artificial life (Alife) evolving autonomous agents and virtual creatures in higher dimensions from a free format representation in the context of neutral networks, gene duplication and the evolution of higher order genetic operators

Evolving an ecology of mathematical expressions with grammatical evolution

This is the author’s version of a work that was accepted for publication in Biosystems. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Biosystems, 111, 2, (2013) DOI: 10.1016/j.biosystems.2012.12.004This paper describes the use of grammatical evolution to obtain an ecology of artificial beings associated with mathematical functions, whose fitness is also defined mathematically. The system allows “parasite” species and “parasites of parasites” to develop, and supports the simultaneous evolution of several ecological niches. The use of standard measurements makes it possible to explore the influence of the number of niches or the presence of parasites on “biological” diversity and similar functions. Our results suggest that some of the features of biological evolution depend more on the genetic substrate and natural selection than on the actual phenotypic expression of that substrate

Evolving a predator–prey ecosystem of mathematical expressions with grammatical evolution

This article describes the use of grammatical evolution to obtain a predator–prey ecosystem of artificial beings associated with mathematical functions, whose fitness is also defined mathematically. The system supports the simultaneous evolution of several ecological niches and through the use of standard measurements, makes it possible to explore the influence of the number of niches and the values of several parameters on ‘‘biological’’ diversity and similar functions. Sensitivity analysis tests have been made to find the effect of assigning different constant values to the genetic parameters that rule the evolution of the system and the predator–prey interaction or of replacing them by functions of time. One of the parameters (predator efficiency) was found to have a critical range, outside which the ecologies are unstable; two others (genetic shortening rate and predator–prey fitness comparison logistic amplitude) are critical just at one side of the range), the others are not critical. The system seems quite robust, even when one or more parameters are made variable during a single experiment, without leaving their critical ranges. Our results also suggest that some of the features of biological evolution depend more on the genetic substrate and natural selection than on the actual phenotypic expression of that substrate. VC 2014 Wiley Periodicals, Inc. Complexity 20: 66–83, 201

Evolving a predator-prey ecosystem of mathematical expressions with grammatical evolution

This is the accepted version of the following article: Alfonseca, M. and Soler Gil, F. J. (2015), Evolving a predator–prey ecosystem of mathematical expressions with grammatical evolution. Complexity, 20: 66–83, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/cplx.21507/abstractThis article describes the use of grammatical evolution to obtain a predator–prey ecosystem of artificial beings associated with mathematical functions, whose fitness is also defined mathematically. The system supports the simultaneous evolution of several ecological niches and through the use of standard measurements, makes it possible to explore the influence of the number of niches and the values of several parameters on “biological” diversity and similar functions. Sensitivity analysis tests have been made to find the effect of assigning different constant values to the genetic parameters that rule the evolution of the system and the predator–prey interaction or of replacing them by functions of time. One of the parameters (predator efficiency) was found to have a critical range, outside which the ecologies are unstable; two others (genetic shortening rate and predator–prey fitness comparison logistic amplitude) are critical just at one side of the range), the others are not critical. The system seems quite robust, even when one or more parameters are made variable during a single experiment, without leaving their critical ranges. Our results also suggest that some of the features of biological evolution depend more on the genetic substrate and natural selection than on the actual phenotypic expression of that substrat