Design by Evolution pp 145-167

Part of the Natural Computing Series book series (NCS) | Cite as

Evolving the Mandelbrot Set to Imitate Figurative Art

  • J. J. Ventrella

Abstract

This chapter describes a technique for generating semi-abstract figurative imagery using variations on the Mandelbrot Set equation, evolved with a genetic algorithm. The Mandelbrot Set offers an infinite supply of complex fractal imagery, but its expressive ability is limited, as far as being material for visual manipulation by artists. The technique described here achieves diverse imagery by manipulating the mathematical function that generates the Set.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ashlock, D.: Evolutionary exploration of the Mandelbrot set. In: Proceedings of the 2006 Congress On Evolutionary Computation, pp. 7432–7439 (2006)Google Scholar
  2. 2.
    eNZed Blue: The Koruandelbrot (2005). http://www.enzedblue.com/Fractals/Fractals.htmlGoogle Scholar
  3. 3.
    Dawkins, R.: The Blind Watchmaker — Why the Evidence of Evolution Reveals a Universe Without Design. W. W. Norton and Company (1986)Google Scholar
  4. 4.
    Dewdney, A.: Computer recreations: a computer microscope zooms in for a look at the most complex object in mathematics. Scientific American pp. 16–25 (1985)Google Scholar
  5. 5.
    Dickerson, R.: Higher-order Mandelbrot fractals: experiments in nanogeometry (2006). http://mathforum.org/library/view/65021.htmlGoogle Scholar
  6. 6.
    Douady, A., Hubbard, J.: Etude dynamique des polynomes complexes, I and II. Publ. Math. Orsay (1984, 1985)Google Scholar
  7. 7.
    Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley (1989)Google Scholar
  8. 8.
    Koza, J.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press (1992)Google Scholar
  9. 9.
    Lakoff, G., Núnez, R.: Where Mathematics Comes From — How the Embodied Mind Brings Mathematics Into Being. Basic Books (2000)Google Scholar
  10. 10.
    Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman and Company (1977)Google Scholar
  11. 11.
    McCormack, J.: Open problems in evolutionary music and art. Lecture Notes in Computer Science 3449, 428–436 (2005)CrossRefGoogle Scholar
  12. 12.
    Peitgen, H., Saupe, D. (eds.): The Science of Fractal Images. Springer-Verlag (1988)Google Scholar
  13. 13.
    Penrose, R.: The Road to Reality, A Complete Guide to the Laws of the Universe, Knopf (2004)Google Scholar
  14. 14.
    Pickover, C.: Computers, Pattern, Chaos, and Beauty — Graphics From an Unseen World. St. Martins Press (1990)Google Scholar
  15. 15.
    Rooke, S.: Eons of genetically evolved algorithmic images. In: P. Bentley, D. Corne (eds.) Creative Evolutionary Systems. Morgan Kaufmann, San Francisco, CA (2001)Google Scholar
  16. 16.
    Sims, K.: Artificial evolution for computer graphics. In: Proceedings of the 18th annual conference on Computer graphics and interactive techniques, pp. 319–328 (1991)Google Scholar
  17. 17.
    Todd, S., Latham, W.: Evolutionary Art and Computers. Academic Press (1992)Google Scholar
  18. 18.
    Ushiki, S.: Phoenix. IEEE Transactions on Circuits and Systems 35(7), 788 (1988)CrossRefGoogle Scholar
  19. 19.
    Ventrella, J.: Explorations in the emergence of morphology and locomotion behaviour in animated characters. In: R. Brooks, P. Maes (eds.) Artificial Life IV — Proceedings of the 4th International Workshop on the Synthesis and Simulation of Living Systems, pp. 436–441. MIT Press (1994)Google Scholar
  20. 20.
    Ventrella, J.: Mandeltweaks (2004). http://www.ventrella.com/Tweaks/MandelTweaks/tweaks.htmlGoogle Scholar
  21. 21.
    Ventrella, J.: Mandelswarm — particle swarm seeks the boundary of the Mandelbrot Set (2005). http://www.ventrella.com/Tweaks/MandelTweaks/MandelSwarm/MandelSwarm.htmlGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • J. J. Ventrella

There are no affiliations available

Personalised recommendations