The Visual Computer

, Volume 26, Issue 12, pp 1467–1483 | Cite as

Interactive evolutionary 3D fractal modeling

  • Wenjun Pang
  • K. C. Hui
Original Article


This paper presents a technique for creating 3D fractal art forms automatically. Using this approach, designers can get access to a large number of 3D art shapes that can be modified interactively. This is based on a modified evolutionary algorithm using Fractal Transform (FT) and Iterated Function System (IFS), which provides tunable geometric parameters. Fitness function for measuring the aesthetics of a fractal shape is formulated based on characteristic parameters in fractal theory, including capacity dimension, correlation dimension, and largest Lyapunov exponent. The productivity of visually appealing fractal can be enhanced by using the proposed technique. Experiments demonstrated the effectiveness of the proposed method, which can be applied to the design of jewelry, light fixture, and decorative patterns.


3D fractal Iterated function system Genetic algorithm Interactive evolutionary design 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barnsley, M., Demko, S.: Iterated function systems and the global construction of fractals. Proc. R. Soc. Lond. A 399(1817), 243–275 (1985) zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Sprott, J.C.: Automatic Generation of iterated function systems. Comput. Graph. 18(3), 417–425 (1994) CrossRefGoogle Scholar
  3. 3.
    Barnsley, M.: Fractals Everywhere, 2nd edn. Academic Press, San Diego (1993) zbMATHGoogle Scholar
  4. 4.
    Scott, D.: The fractal flame algorithm 2004
  5. 5.
    Scott, D.: The electric sheep. ACM SIGEVOlution 1(2), 10–16 (2006) CrossRefGoogle Scholar
  6. 6.
    Wannarumon, S., Bohez, E.L.J.: A new aesthetic evolutionary approach for jewelry design. Comput.-Aided Des. Appl. 3(4), 385–394 (2006) Google Scholar
  7. 7.
    Wannarumon, S., Bohez, E.L.J., Annanon, K.: Aesthetic evolutionary algorithm for fractal-based user-centered jewelry design. AI EDAM 22(1), 19–39 (2008) Google Scholar
  8. 8.
    Berkowitz, J.: Fractal Cosmos: The Art of Mathematical Design. Amber Lotus, Portland (1998) Google Scholar
  9. 9.
    Joye, Y.: Evolutionary and cognitive motivations for fractal art in art and design education. Int. J. Art Des. Education 24(2), 175–185 (2005) CrossRefGoogle Scholar
  10. 10.
    Aks, D., Sprott, J.C.: Quantifying aesthetic preference for chaotic patterns. Empir. Stud. Arts 14, 1–16 (1996) Google Scholar
  11. 11.
    Spehar, B., Clifford, C.W.G., Newell, B.R., Taylor, R.P.: Universal aesthetic of fractals. Comput. Graph. 27(5), 813–820 (2003) CrossRefGoogle Scholar
  12. 12.
    Mitina, O.V., Abraham, F.D.: The use of fractals for the study of the psychology of perception: psychophysics and personality factors, a brief report. Int. J. Mod. Phys. C 4(8), 1047–1060 (2003) CrossRefGoogle Scholar
  13. 13.
    Bentley, P.: Evolutionary Design by Computers. Morgan Kaufmann, San Francisco (1999) zbMATHGoogle Scholar
  14. 14.
    Todd, S., Latham, W.: Evolutionary Art and Computers. Academic Press, London (1992) zbMATHGoogle Scholar
  15. 15.
    Sims, K.: Artificial evolution for computer graphics. Comput. Graph. 25(4), 319–328 (1991) CrossRefMathSciNetGoogle Scholar
  16. 16.
    Kruger, A.: Implementation of a fast box-counting algorithm. Comput. Phys. Commun. 98(1–2), 224–234 (1996) zbMATHCrossRefGoogle Scholar
  17. 17.
    Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenom. 9(1–2), 189–208 (1983) zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Merkwirth, C., Parlitz, U., Wedekind, I., Lauterborn, W.: TSTOOL MatLAB toolbox, (2002)
  19. 19.
    Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57(3), 617–656 (1985) CrossRefMathSciNetGoogle Scholar
  20. 20.
    Jacob, C.: A power primer. Psycholog. Bull. 112(1), 55–159 (1992) Google Scholar
  21. 21.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. ACM Comput. Graph. 21(3), 163–169 (1987) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.CAD Laboratory, Department of Mechanical and Automation EngineeringChinese University of Hong KongHong KongChina

Personalised recommendations