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SELF-SIMILARITY OF 𠒫-POSITIONS OF (2n + 1)-DIMENSIONAL WYTHOFF’S GAME

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Listed:
  • YANXI LI

    (School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China)

  • WEN WU

    (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 (2n + 1)-dimensional Wythoff’s game; that is the Wythoff’s game with (2n + 1) heaps. We characterize their 𠒫-positions explicitly and show that they have self-similar structures. In particular, the set of all 𠒫-positions of 3-dimensional Wythoff’s game generates the well-known fractal set — the Sierpinski sponge.

Suggested Citation

  • Yanxi Li & Wen Wu, 2021. "SELF-SIMILARITY OF ð ’«-POSITIONS OF (2n + 1)-DIMENSIONAL WYTHOFF’S GAME," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-8, May.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x21500614
    DOI: 10.1142/S0218348X21500614
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    Keywords

    Wythoff’s Game; Sierpinski Sponge;

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