The number of paperfolding curves in a covering of the plane

DOI10.32917/HMJ/1492048844zbMATH Open1378.52021arXiv1408.3038OpenAlexW2962897763WikidataQ128867155 ScholiaQ128867155MaRDI QIDQ2357385

Francis Oger

Publication date: 13 June 2017

Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)

Abstract: These results complete our paper in Hiroshima Mathematical Journal, vol. 42, pp. 37-75. Let C be a covering of the plane by disjoint complete folding curves which satisfies the local isomorphism property. We show that C is locally isomorphic to an essentially unique covering generated by an $infty$-folding curve. We prove that C necessarily consists of 1, 2, 3, 4 or 6 curves. We give examples for each case; the last one is realized if and only if C is generated by the alternating folding curve or one of its successive antiderivatives. We also extend the results of our previous paper to another class of paperfolding curves introduced by M. Dekking.

Full work available at URL: https://arxiv.org/abs/1408.3038

zbMATH Keywords

coveringlocal isomorphismpaperfolding curve

Mathematics Subject Classification ID

Geometric constructions in real or complex geometry (51M15) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

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