Affiliation:
1. School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China
Abstract
Wythoff’s game as a classic combinatorial game has been well studied. In this paper, we focus on [Formula: see text]-dimensional Wythoff’s game; that is the Wythoff’s game with [Formula: see text] heaps. We characterize their [Formula: see text]-positions explicitly and show that they have self-similar structures. In particular, the set of all [Formula: see text]-positions of 3-dimensional Wythoff’s game generates the well-known fractal set — the Sierpinski sponge.
Funder
Fundamental Research Funds for the Central Universities
Natural Science Foundation of Guangdong Province
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation