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.