Emergence of the Sierpinski Gasket in Coin-Dividing Problems
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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.
KeywordsFractal Coin dividing Sierpinski gasket Dynamical system Chaos game
The author is grateful to Dr. Makoto Katori, Dr. Yoshihiro Yamazaki, and Dr. Jun-ichi Wakita for their fruitful and stimulating discussions and comments.