Self-avoiding space-filling folding curves in dimension 3

2025/01/12 by Francis Oger, Oger, Francis
Computer Science · Engineering · Mathematics · #05B45 (Primary) 52C22 #52C23 (Secondary) #Advanced Materials and Mechanics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2501.06888

openalex publication_date 2025/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Various examples of folding curves in R² have been considered: dragons and other square curves, terdragons and other triangular curves, Peano-Gosper curves based on hexagons. They are self-avoiding. They form coverings of R², by one curve or by a small number of curves, which satisfy the local isomorphism property. They were used to define some fractals. We construct an example with similar properties in R³.

Related

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