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Fractal behind coin-reducing payment

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  • Yamamoto, Ken
  • Yamazaki, Yoshihiro

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.

Suggested Citation

  • Yamamoto, Ken & Yamazaki, Yoshihiro, 2012. "Fractal behind coin-reducing payment," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1058-1066.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:8:p:1058-1066
    DOI: 10.1016/j.chaos.2012.05.004
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    Cited by:

    1. Yamamoto, Ken, 2014. "Fractal patterns related to dividing coins," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 51-57.

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