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Journal of the Korean Physical Society

, Volume 66, Issue 10, pp 1617–1622 | Cite as

Analysis of multifractal strengths in game behaviors

  • Cheol-Hwan You
  • Dong-In Lee
  • Kyungsik Kim
Brief Reports

Abstract

In this paper, we study the multifractal structure and its property from the number of end stones, which means the number of stones on the board at the end of a game, in the Baduk game. We mainly estimate the generalized Hurst exponent, the Renyi exponent, and the singularity spectrum for the time-series data of the number of end stones via multifractal detrended fluctuation analysis. For three segments, we mainly simulate and analyze the multifractal strength in Baduk games with four players. Particularly, the results obtained for games with four players are compared to each other and analyzed in detail.

Keywords

Generalized Hurst exponent Renyi exponent Singularity spectrum Multifractal strength Baduk game 

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References

  1. [1]
    A.-L. Barabasi and H. E. Stanley, Fractional Concepts in Surface Growth (Cambridge University Press, New York, 1995).CrossRefGoogle Scholar
  2. [2]
    B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1983).Google Scholar
  3. [3]
    A. L. Windus and H. J. Jensen, Physica A 388, 3107 (2009).ADSCrossRefGoogle Scholar
  4. [4]
    T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1988).Google Scholar
  5. [5]
    G. Paladin and A. Vulpiani, Phys. Rep. 156, 147 (1987).MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    H. G. E. Hentschel and I. Procaccia, Physica D 8, 435 (1983).zbMATHMathSciNetADSCrossRefGoogle Scholar
  7. [7]
    A. Nobi, S. E.Maeng, G.G. Ha and J. W. Lee, J. Korean Phys. Soc. 62, 569 (2013)ADSCrossRefGoogle Scholar
  8. [7a]
    M. W. Cho, J. Korean Phys. Soc. 64, 1213 (2014)ADSCrossRefGoogle Scholar
  9. [7b]
    H. W. Choi, S. E. Maeng and J. W. Lee, J. Korean Phys. Soc. 60, 657 (2012).ADSCrossRefGoogle Scholar
  10. [8]
    C. Beck and F. Schögl, Thermodynamics of chaotic systems (Cambridge University Press, 1993)CrossRefGoogle Scholar
  11. [8a]
    G. Lim, S. Y. Kim, H. Lee, K. Kim and D.-I. Lee, Physica A 386, 259 (2007).ADSCrossRefGoogle Scholar
  12. [9]
    G. Parasi and U. Frisch, in Proceedings of the International School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by P. Huerre and P. Coullet (Plenum, New York, 1988).Google Scholar
  13. [10]
    J. W. Kantelhardt, S. A. Zschiegner, E. K-Bunde, S. Havlin, A. Bunde and H. E. Stanley, Physica A 316, 87 (2002).zbMATHADSCrossRefGoogle Scholar
  14. [11]
    C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley and A. L. Goldberger, Phys. Rev. E 49, 1685 (1994).ADSCrossRefGoogle Scholar
  15. [12]
    S. M. Ossadnik, S. B. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, C.-K. Peng, M. Simons and H. E. Stanley, Biophys. J. 67, 64 (1994).ADSCrossRefGoogle Scholar
  16. [13]
    Z. Eisler, J. Kertesz, S.-H. Yook and A.-L. Barabasi, Europhys. Lett. 69, 664 (2005).ADSCrossRefGoogle Scholar
  17. [14]
    Z. Eisler and J. Kertesz, Europhys. Lett. 77, 28001 (2007).ADSCrossRefGoogle Scholar
  18. [15]
    Z.-Q. Jiang, L. Guo and W.-X. Zhou, Eur. Phys. J. B 57, 347 (2007).ADSCrossRefGoogle Scholar
  19. [16]
    N. Vandewalle and M. Ausloos, Eur. Phys. J. B 4, 257 (1998).ADSCrossRefGoogle Scholar
  20. [17]
    K. Ivanova and M. Ausloos, Eur. Phys. J. B 8, 665 (1999).ADSCrossRefGoogle Scholar
  21. [18]
    F. Schmitt, D. Schertzer and S. Lovejoy, Appl. Stoch. Models Data Anal. 15, 29 (1999).zbMATHCrossRefGoogle Scholar
  22. [19]
    F. Schmitt, D. Schertzer and S. Lovejoy, Appl. Fin. 3, 361 (2000).zbMATHGoogle Scholar
  23. [20]
    L. Calvet and A. Fisher, Rev. Econ. Stat. 84, 381 (2002).CrossRefGoogle Scholar
  24. [21]
    M. Ausloos and K. Ivanova, Comp. Phys. Comm. 147, 582 (2002).zbMATHADSCrossRefGoogle Scholar
  25. [22]
    A. Z. Gorski, S. Drozdz and J. Speth, Physica A 316, 496 (2002).zbMATHADSCrossRefGoogle Scholar
  26. [23]
    J. Alvarez-Ramirez, M. Cisneros, C. Ibarra-Valdez and A. Soriano, Physica A 313, 651 (2002).zbMATHADSCrossRefGoogle Scholar
  27. [24]
    M. Balcilar, Emerging Markets Fin. Trade 39, 5 (2003).Google Scholar
  28. [25]
    K. E. Lee and J. W. Lee, J. Korean Phys. Soc. 46, 726 (2005).Google Scholar
  29. [26]
    J. W. Lee, K. E. Lee and P. A. Rikvold, Physica A 364, 355 (2006).ADSCrossRefGoogle Scholar
  30. [27]
    Z.-Q. Jiang and W.-X. Zhou, Physica A 381, 343 (2007).ADSCrossRefGoogle Scholar
  31. [28]
    X. Sun, H.-P. Chen, Z.-Q. Wu and Y.-Z. Yuan, Physica A 291, 553 (2001).zbMATHADSCrossRefGoogle Scholar
  32. [29]
    X. Sun, H.-P. Chen, Y.-Z. Yuan and Z.-Q. Wu, Physica A 301, 473 (2001).zbMATHADSCrossRefGoogle Scholar
  33. [30]
    D.-S. Ho, C.-K. Lee, C.-C. Wang and M. Chuang, Physica A 332, 448 (2004).ADSCrossRefGoogle Scholar
  34. [31]
    Y. Wei and D.-S. Huang, Physica A 355, 497 (2005).ADSCrossRefGoogle Scholar
  35. [32]
    G.-F. Gu, W. Chen and W.-X. Zhou, Eur. Phys. J. B 57, 81 (2007).ADSCrossRefGoogle Scholar
  36. [33]
    X.-T. Zhuang and Y. Yuan, Physica A 387, 511 (2008).ADSCrossRefGoogle Scholar
  37. [34]
    G.-X. Du and X.-X. Ning, Physica A 387, 261 (2008).ADSCrossRefGoogle Scholar
  38. [35]
    Z. R. Struzik and A. P. J. M. Siebes, Physica A 309, 388 (2002).zbMATHADSCrossRefGoogle Scholar
  39. [36]
    A. Turiel and C. J. Perez-Vicente, Physica A 322, 629 (2003).zbMATHMathSciNetADSCrossRefGoogle Scholar
  40. [37]
    A. Turiel and C. J. Perez-Vicente, Physica A 355, 475 (2005).ADSCrossRefGoogle Scholar
  41. [38]
    P. Oswiecimka, J. Kwapien, S. Drozdz and R. Rak, Acta Physica Polonica B 36, 2447 (2005).ADSGoogle Scholar
  42. [39]
    M. Ausloos, Phys. Rev. E 86, 031108 (2012).ADSCrossRefGoogle Scholar
  43. [40]
    M. Cencini, F. Cencini and A. Vulpiani, Chaos: From Models to Complex Systems (World Scientific, Singapore, 2010).Google Scholar

Copyright information

© The Korean Physical Society 2015

Authors and Affiliations

  1. 1.Department of Environmental Atmospheric SciencesPukyong National UniversityBusanKorea
  2. 2.Department of PhysicsPukyong National UniversityBusanKorea

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