TY - JOUR
T1 - Fractal behind coin-reducing payment
AU - Yamamoto, Ken
AU - Yamazaki, Yoshihiro
N1 - Funding Information:
The authors are very grateful to Dr. Mitsugu Matsushita and Dr. Hiroto Kuninaka for their beneficial comments. The present work was partially supported by Grant-in-Aid for JSPS Fellows from the Japan Society for the Promotion of Science.
PY - 2012/8
Y1 - 2012/8
N2 - The 'minimal' payment - a payment method which minimizes the number of coins in a purse - is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. By using the delay plot, the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the average number of coins in a purse, and conclude that the minimal-payment strategy is the best to reduce the number of coins in a purse. Moreover, we compare our results to the rule-60 cellular automaton and the Pascal-Sierpinski gaskets, which are known as generators of the discrete Sierpinski gasket.
AB - The 'minimal' payment - a payment method which minimizes the number of coins in a purse - is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. By using the delay plot, the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the average number of coins in a purse, and conclude that the minimal-payment strategy is the best to reduce the number of coins in a purse. Moreover, we compare our results to the rule-60 cellular automaton and the Pascal-Sierpinski gaskets, which are known as generators of the discrete Sierpinski gasket.
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U2 - 10.1016/j.chaos.2012.05.004
DO - 10.1016/j.chaos.2012.05.004
M3 - Article
AN - SCOPUS:84861873203
SN - 0960-0779
VL - 45
SP - 1058
EP - 1066
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 8
ER -