Sandpile model
In 1987 Per Bak, Chao Tang and Kurt Wiesenfeld proposed a simple cellular automaton, sandpile model, which exhibits critical behavior [1, 2, 3]. In this critical behavior state small perturbations acting upon the system may cause huge consequences or go completely unnoticed. The impact of these consequences seems to follow power-law distribution.
In this text we will briefly discuss how the model works and present interactive applet. We would like to draw your attention to a previous article in which described earthquake model.
How model works
Here we have a grid of certain size. Each site on the grid, cell, represents small sandpile. During each time step we randomly place a grain of sand on the grid, thus increasing steepness of certain random sanpile. If sandpile reaches critical steepness, it shares some of its sand with neighboring sandpiles. Those may also reach critical steepness and further share the sand with its neighbors. The chain reaction goes on until no critical sandpiles remain. All sandpiles, which were in critical state at given time, are assumed to belong to a single landslide.
Interestingly landslide sizes, \( S \), have stationary distribution which is power-law. We invite you to confirm this using the applet below.
HTML5 applet
References
- P. Bak, C. Tang, K. Wiesenfeld. Self-organized criticality. Physical Review Letters 59: 381-384 (1987).
- H. J. Jensen, K. Christensen, H. C. Fogedby. 1/f noise, distribution of lifetimes, and a pile of sand. Physical Review B 40: 7425-7427 (1989). doi: 10.1103/PhysRevB.40.7425.
- J. Kertesz, L. B. Kiss. The noise spectrum in the model of self-organised criticality. Journal of Physics A 23: L433 (1990).
