Fractal behind coin-reducing payment

Ken Yamamoto, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    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
    Volume45
    Issue number8
    DOIs
    Publication statusPublished - 2012 Aug

    Fingerprint

    Fractal
    Sierpinski Gasket
    Pascal
    Fine Structure
    Cellular Automata
    Time series
    Generator
    Minimise
    Estimate

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Fractal behind coin-reducing payment. / Yamamoto, Ken; Yamazaki, Yoshihiro.

    In: Chaos, Solitons and Fractals, Vol. 45, No. 8, 08.2012, p. 1058-1066.

    Research output: Contribution to journalArticle

    Yamamoto, Ken ; Yamazaki, Yoshihiro. / Fractal behind coin-reducing payment. In: Chaos, Solitons and Fractals. 2012 ; Vol. 45, No. 8. pp. 1058-1066.
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