Multifractal aspects of an efficient change-making process

Ken Yamamoto, Yoshihiro Yamazaki

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper, we focus on the «minimal payment» which minimizes the number of coins left after the payment. Two kinds of multifractal properties of the minimal payment are studied. The first one is a frequency distribution of change amounts, and the second one is a visiting probability on the delay plot of successive change amounts. When the face values of coins are power of two (1, 2, 4, 8, ...), we find that these two distributions are related to well-known multifractal models, and derive analytical expressions of multifractal spectra.

Original languageEnglish
Article number1350014
Issue number2
Publication statusPublished - 2013 Jun


  • Change-Making Process
  • Delay Plot
  • Multifractal

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geometry and Topology
  • Applied Mathematics


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