Fractal behind coin-reducing payment

Ken Yamamoto*, Yoshihiro Yamazaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1058-1066
Number of pages9
JournalChaos, solitons and fractals
Issue number8
Publication statusPublished - 2012 Aug

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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