TY - JOUR
T1 - Multifractal aspects of an efficient change-making process
AU - Yamamoto, Ken
AU - Yamazaki, Yoshihiro
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - Change-Making Process
KW - Delay Plot
KW - Multifractal
UR - http://www.scopus.com/inward/record.url?scp=84880996781&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84880996781&partnerID=8YFLogxK
U2 - 10.1142/S0218348X1350014X
DO - 10.1142/S0218348X1350014X
M3 - Article
AN - SCOPUS:84880996781
VL - 21
JO - Fractals
JF - Fractals
SN - 0218-348X
IS - 2
M1 - 1350014
ER -