English

Plane-filling curves on all uniform grids

Combinatorics 2018-07-04 v2

Abstract

We describe a search for plane-filling curves traversing all edges of a grid once. The curves are given by Lindenmayer systems with only one non-constant letter. All such curves for small orders on three grids have been found. For all uniform grids we show how curves traversing all points once can be obtained from the curves found. Curves traversing all edges once are described for the four uniform grids where they exist.

Keywords

Cite

@article{arxiv.1607.02433,
  title  = {Plane-filling curves on all uniform grids},
  author = {Jörg Arndt},
  journal= {arXiv preprint arXiv:1607.02433},
  year   = {2018}
}

Comments

124 figures, many in color; corrected counts for shapes on the triangular grid

R2 v1 2026-06-22T14:49:27.723Z