Fractal behind coin-reducing payment

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.

► Our purses sometimes get heavy by many coins.
► We present a payment method that minimizes the number of coins left in a purse.
► An ordered fractal-like pattern arises in this payment process.
► Relevance to other fractal models is discussed.