English

Fractal behind smart shopping

Discrete Mathematics 2012-07-04 v1 Cellular Automata and Lattice Gases

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.

Cite

@article{arxiv.1103.1208,
  title  = {Fractal behind smart shopping},
  author = {Ken Yamamoto and Yoshihiro Yamazaki},
  journal= {arXiv preprint arXiv:1103.1208},
  year   = {2012}
}

Comments

16 pages

R2 v1 2026-06-21T17:35:54.069Z