Journal of Statistical Physics

, Volume 152, Issue 3, pp 534–540 | Cite as

Emergence of the Sierpinski Gasket in Coin-Dividing Problems



The present paper proposes a generation mechanism of a fractal pattern related to a coin system. The problem is formulated in terms of a situation of dividing coins among people. Remarkably, a fractal pattern like the Sierpinski gasket is obtained, by marking all the possible division of coins as a point set. The mechanism for this fractal structure is reduced to nested relations, owing to a hierarchical property of coin denominations. Relevance to dynamical systems is also discussed.


Fractal Coin dividing Sierpinski gasket Dynamical system Chaos game 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Science and EngineeringChuo UniversityTokyoJapan

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