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Evolving the Mandelbrot Set to Imitate Figurative Art

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Part of the book series: Natural Computing Series ((NCS))

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.

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References

  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. eNZed Blue: The Koruandelbrot (2005). http://www.enzedblue.com/Fractals/Fractals.html

    Google Scholar 

  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. 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. Dickerson, R.: Higher-order Mandelbrot fractals: experiments in nanogeometry (2006). http://mathforum.org/library/view/65021.html

    Google Scholar 

  6. Douady, A., Hubbard, J.: Etude dynamique des polynomes complexes, I and II. Publ. Math. Orsay (1984, 1985)

    Google Scholar 

  7. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley (1989)

    Google Scholar 

  8. Koza, J.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press (1992)

    Google Scholar 

  9. Lakoff, G., Núnez, R.: Where Mathematics Comes From — How the Embodied Mind Brings Mathematics Into Being. Basic Books (2000)

    Google Scholar 

  10. Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman and Company (1977)

    Google Scholar 

  11. McCormack, J.: Open problems in evolutionary music and art. Lecture Notes in Computer Science 3449, 428–436 (2005)

    Article  Google Scholar 

  12. Peitgen, H., Saupe, D. (eds.): The Science of Fractal Images. Springer-Verlag (1988)

    Google Scholar 

  13. Penrose, R.: The Road to Reality, A Complete Guide to the Laws of the Universe, Knopf (2004)

    Google Scholar 

  14. Pickover, C.: Computers, Pattern, Chaos, and Beauty — Graphics From an Unseen World. St. Martins Press (1990)

    Google Scholar 

  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. 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. Todd, S., Latham, W.: Evolutionary Art and Computers. Academic Press (1992)

    Google Scholar 

  18. Ushiki, S.: Phoenix. IEEE Transactions on Circuits and Systems 35(7), 788 (1988)

    Article  Google Scholar 

  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. Ventrella, J.: Mandeltweaks (2004). http://www.ventrella.com/Tweaks/MandelTweaks/tweaks.html

    Google Scholar 

  21. Ventrella, J.: Mandelswarm — particle swarm seeks the boundary of the Mandelbrot Set (2005). http://www.ventrella.com/Tweaks/MandelTweaks/MandelSwarm/MandelSwarm.html

    Google Scholar 

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© 2008 Springer-Verlag Berlin Heidelberg

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Ventrella, J.J. (2008). Evolving the Mandelbrot Set to Imitate Figurative Art. In: Hingston, P.F., Barone, L.C., Michalewicz, Z. (eds) Design by Evolution. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74111-4_9

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  • DOI: https://doi.org/10.1007/978-3-540-74111-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74109-1

  • Online ISBN: 978-3-540-74111-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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