The European Physical Journal B

, 87:41

Emergence of self-similarity in football dynamics

  • Akifumi Kijima
  • Keiko Yokoyama
  • Hiroyuki Shima
  • Yuji Yamamoto
Open AccessRegular Article

DOI: 10.1140/epjb/e2014-40987-5

Cite this article as:
Kijima, A., Yokoyama, K., Shima, H. et al. Eur. Phys. J. B (2014) 87: 41. doi:10.1140/epjb/e2014-40987-5


The multiplayer dynamics of a football game is analyzed to unveil self-similarities in the time evolution of player and ball positioning. Temporal fluctuations in both the team-turf boundary and the ball location are uncovered to follow the rules of fractional Brownian motion with a Hurst exponent of H ~ 0.7. The persistence time below which self-similarity holds is found to be several tens of seconds, implying a characteristic time scale that governs far-from-equilibrium motion on a playing field.


Statistical and Nonlinear Physics
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© The Author(s) 2014

Authors and Affiliations

  • Akifumi Kijima
    • 1
  • Keiko Yokoyama
    • 2
    • 3
  • Hiroyuki Shima
    • 4
  • Yuji Yamamoto
    • 5
  1. 1.Graduate School of Education, University of YamanashiYamanashiJapan
  2. 2.Division of Applied Physics, Faculty of Engineering, Hokkaido UniversityHokkaidoJapan
  3. 3.Japan Society for the Promotion of ScienceTokyoJapan
  4. 4.Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and EngineeringUniversity of YamanashiYamanashiJapan
  5. 5.Research Center of Health, Physical Fitness and Sports & Department of Psychology and Human Developmental Sciences, Nagoya UniversityNagoyaJapan