Emergence of self-similarity in football dynamics
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- Kijima, A., Yokoyama, K., Shima, H. et al. Eur. Phys. J. B (2014) 87: 41. doi:10.1140/epjb/e2014-40987-5
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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.