Interesting Esoterica

Plane-filling curves on all uniform grids

Article by Jörg Arndt
  • Published in 2016
  • Added on
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.

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BibTeX entry

@article{Planefillingcurvesonalluniformgrids,
	title = {Plane-filling curves on all uniform grids},
	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.},
	url = {http://arxiv.org/abs/1607.02433v2 http://arxiv.org/pdf/1607.02433v2},
	year = 2016,
	author = {J{\"{o}}rg Arndt},
	comment = {},
	urldate = {2020-09-21},
	archivePrefix = {arXiv},
	eprint = {1607.02433},
	primaryClass = {math.CO},
	collections = {fun-maths-facts,geometry,things-to-make-and-do}
}