TL;DR
This paper explores the fractal structure of minimal payment change sequences, demonstrating their similarity to the Sierpinski gasket and showing the method's effectiveness in reducing coins in a purse.
Contribution
It introduces a minimal payment method analyzed through fractal geometry, revealing its connection to Sierpinski structures and its efficiency in coin reduction.
Findings
Minimal payment reduces the average number of coins in a purse.
Change sequences exhibit fractal structures similar to the Sierpinski gasket.
The method outperforms other strategies in coin minimization.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.