Fractal behind coin-reducing payment

Ken Yamamoto, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    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

    • Mathematics(all)

    Cite this