Grammatical evolution to design fractal curves with a given dimension

IBM Journal of Research and Development

Volumn 47, Issue 4, 2003, Pages 483-493

  Ortega, Alfonso ^a   Dalhoum, Abdellatif Abu ^a   Alfonseca, Manuel ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; FRACTALS; MATHEMATICAL MODELS; VECTORS;

FRACTAL CURVES; GRAMMATICAL EVOLUTION; LINDENMAYER GRAMMARS;

COMPUTATIONAL GRAMMARS;

EID: 0042823951     PISSN: 00188646     EISSN: None     Source Type: Journal    
DOI: 10.1147/rd.474.0483     Document Type: Article

References (36)

1. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York, 1977.
2. K. Mela and J. N. Louie, "Correlation Length and Fractal Dimension Interpretation from Seismic Data Using Variograms and Power Spectra," Geophysics 66, No. 5, 1372-1378 (2001).
3. R. P. Taylor, B. Spehar, C. W. G. Clifford, and B. R. Newell, "The Visual Complexity of Pollock's Dripped Fractals," Proceedings of the International Conference of Complex Systems, 2002; see also http://materialscience.uoregon.edu/taylor/art/Taylor1CCS2002.pdf.
4. P. M. Iannaccone and M. Khokha, Eds., Fractal Geometry in Biological Systems: An Analytical Approach, CRC Press, Boca Raton, FL, 1996.
5. W. Bauer and C. D. Mackenzie, "Cancer Detection via Determination of Fractal Cell Dimension," presented at the Workshop on Computational and Theoretical Biology, Michigan State University, April 24, 1999; see also http://www.pa.msu.edu/~/bauer/cancer/cancer.pdf.
6. K. Danzer, J. F. van Staden, and D. T. Burns, "Concepts and Applications of the Term 'Dimensionality' in Analytical Chemistry," Pure Appl. Chem. 74, No. 8, 1479-1487 (2002).
7. F. Torrens, "Fractals Hybrid Orbitals in Protein Models," Complexity International 8 (2001); see http://www.csu.edu.au/ci/val108/torren01/.
8. S. Mondoloni and D. Liang, "Airspace Fractal Dimension and Applications," presented at the Third USA/Europe ATM R & D Seminar, 2001.
9. K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan "Hilbert Curve Fractal Antenna: A Small Resonant Antenna for VHF/UHF Applications," Microwave & Opt. Technol. Lett. 29, No. 4, 215-219 (2001).
10. A. Lindenmayer, "Mathematical Models for Cellular Interactions in Development" (in two parts), J. Theor. Biol. 18, 280-315 (1968).
11. G. Herman and G. Rozenberg, Developmental Systems and Languages, North-Holland, Amsterdam, 1975.
12. E. G. Giessmann, "Generation of Fractal Curves by Generalization of Lindenmayer's L Systems," Proceedings of the First IFIP Conference on Fractals in the Fundamental and Applied Sciences, H. O. Peitgen, J. M. Henriques, and L. F. Penedo, Eds., North-Holland, Amsterdam, 1991, pp. 147-157.
13. P. Prusinkiewicz, "Graphical Applications of L-Systems," Proceedings of Graphics Interface 86 and Vision Interface 86, M. Wein and E. M. Kidd, Eds., Vancouver, BC, 1986, pp. 247-253.
14. M. Alfonseca and A. Ortega, "A Study of the Representation of Fractal Curves by L Systems and Their Equivalences," IBM J. Res. & Dev. 41, No. 6, 727-736 (1997).
15. M. Alfonseca and A. Ortega, "Representation of Some Cellular Automata by Means of Equivalent L Systems," Complexity International 7, 1-16 (2000), ISSN: 1320-0682; see http://www.csu.edu.au/ci/vol07/alfons01/.
16. J. D. Corbit and D. J. Garbary, "Computer Simulation of the Morphology and Development of Several Species of Seaweed Using Lindenmayer Systems," Comput. & Graph. 17, No. 1, 85-88 (1993).
17. G. Rozenberg and A. Salomaa, Eds., Lindenmayer Systems. Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology, Springer-Verlag, Berlin, 1992.
18. M. Alfonseca and A. Oretega, "Using APL2 to Compute the Dimension of a Fractal Represented as a Grammar," APL Quote Quad 30, No. 4, 13-23 (2000).
19. M. Alfonseca and A. Ortega, "Determination of Fractal Dimensions from Equivalent L Systems," IBM J. Res. & Dev. 45, No. 6, 797-805 (2001).
20. B. Guiheneuf, S. Jaffard, and J. L. Vehel, "Two Results Concerning Chirps and 2-Microlocal Exponents Prescription," Appl. & Computational Harmonic Anal. 5, 487-492 (1998).
21. K. Daoudi, J. L. Vehel, and Y. Meyer, "Construction of Continuous Functions with Prescribed Local Regularity," J. Constructive Approximation 14, No. 3, 349-385 (1998).
22. S. Jaffard, "Functions with Prescribed Holder Exponent," Appl. & Computational Harmonic Anal. 2, No. 4, 400-401 (1995).
23. M. O'Neill and C. Ryan, "Grammatical Evolution," IEEE Trans. Evolutionary Computation 5, No. 4, 349-358 (2001).
24. M. O'Neill and C. Ryan, "Evolving Multi-Line Compilable C Programs," Proceedings of the Second European Workshop on Genetic Programming (EuroGP'99), 1999; lecture notes in Computer Science 1598, 83-92 (1999).
25. M. O'Neill and C. Ryan, "Under the Hood of Grammatical Evolution," Proceedings of the Genetic and Evolutionary Computation Conference (GECCO'99), W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith, Eds., Morgan Kaufmann Publishers, San Mateo, CA, 1999, pp. 1143-1148.
26. M. O'Neill and C. Ryan, "Genetic Code Degeneracy: Implications for Grammatical Evolution and Beyond," Proceedings of the Fifth European Conference on Artificial Life (ECAL'99), 1999, pp. 149-153.
27. C. Ryan, J. J. Collins, and M. O'Neill, "Grammatical Evolution: Evolving Programs for an Arbitrary Language," Proceedings of the First European Workshop on Genetic Programming (EuroGP'98), 1998; lecture notes in Computer Science 1391, 83-95 (1998).
28. C. Ryan and M. O'Neill, "Grammatical Evolution: A Steady State Approach," Proceedings of the Joint Conference on Information Sciences, 1998, pp. 419-423.
29. C. Ryan and M. O'Neill, "Grammatical Evolution: A Steady State Approach," Proceedings of the Third Annual Genetic Programming Conference (GP'98), J. R. Koza, W. Banzhaf, L. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. L. Riolo, Eds., Morgan Kaufmann Publishers, San Francisco, 1998, pp. 180-185.
30. C. Ryan, M. O'Neill, and J. J. Collins, "Grammatical Evolution: Solving Trigonometric Identities," Proceedings of the Fourth International Conference on Genetic Algorithms, Optimization Problems, Fuzzy Logic, Neural Networks, and Rough Sets (Mended'98), 1998, pp. 111-119.
31. M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, Oxford, England, 1983.
32. G. Ochoa, "On Genetic Algorithms and Lindenmayer Systems," Proceedings of Parallel Problem Solving from Nature, International Conference on Evolutionary Computation (PPSN IV), 1998; lecture notes in Computer Science 1498, 335-343 (1998).
33. G. S. Hornby, Generative Representations for Evolutionary Design Automation, a dissertation presented to the faculty of the Graduate School of Arts and Sciences, Bradeis University Department of Computer Science (Jordan B. Pollack, Advisor) in partial fulfillment of the requirements for the Ph.D. degree, 2003.
34. C. Jacob, "Genetic L-System Programming," Proceedings of Parallel Problem Solving from Nature, the International Conference on Evolutionary Computation (PPSN III), 1994, Springer-Verlag, Berlin; lecture notes in Computer Science 866, 334-343 (1994).
35. C. Traxler and M. Gervautz, "Using Genetic Algorithms to Improve the Visual Quality of Fractal Plants Generated with CSG-PL Systems," Proceedings of the Fourth International Conference in Central Europe on Computer Graphics and Visualization, N. Magnenat-Thalmann and V. Skala, Eds., University of West Bohemia, Plzen, Czech Republic, 1996.
36. A. Ortega, M. de la Cruz, and M. Alfonseca, "Parametric 2-Dimensional L Systems and Recursive Fractal Images: Mandelbrot Set, Julia Sets and Biomorphs," Comput. & Graph. 26, No. 1, 143-149 (2002).