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arXiv · 1103.1208

Fractal behind smart shopping

Ken Yamamoto·Yoshihiro Yamazaki
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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. The delay plot shows visually that 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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Ken Yamamoto, Yoshihiro Yamazaki. 2011-03-07. Fractal behind smart shopping. https://doi.org/10.1016/j.chaos.2012.05.004

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