Application of Genetic Algorithm to Hausdorff Measure Estimation of Sierpinski Carpet

  • Qili Xiao
  • Lifeng Xi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4693)


In this paper, we discuss the realization of the genetic algorithm on calculating the Hausdorff measure of the Sierpinski gasket with compression ratio 1/2 in detail, mainly including the encoding and decoding method, generation of the initial population, and fitness computation. The experimental results prove that the genetic algorithm is an effective and universal method to calculate Hausdorff measure.


Genetic algorithm Sierpinski gasket Hausdorff measure binary string initial population 


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  1. 1.
    Ming, Z., Shudong, S.: Theory and Application of Genetic Algorithm. National Defence Industry Press, Beijing (2002)Google Scholar
  2. 2.
    Guoliang, C., Xufa, W.: Genetic Algorithm and Its Application. People Post Publishing Company, Beijing (2001)Google Scholar
  3. 3.
    Xiaoping, W., Liming, C.: Theory, Application and Software Realization of Genetic Algorithm. Publishing Company of Xi’an Jiaotong University, Xi’an (2002)Google Scholar
  4. 4.
    Lifeng, X., Zhongdi, C.: Some Front Problems of Fractal—Computation of Hausdorff Measure. Journal of Zhejiang Wanli University 14, 1–3 (2001)Google Scholar
  5. 5.
    Zuoling, Z.: Hausdorff Measure of Sierpinski Gasket. Science in China (A) 40, 1016–1021 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Zuoling, Z.: Hausdorff Measure of Self-similar set. Science in China (A) 28, 103–107 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Qili Xiao
    • 1
  • Lifeng Xi
    • 1
  1. 1.School of Computer Science and Information Technology, Zhejiang Wanli University, Ningbo, Zhejiang, 315100P.R. China

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