Slopes of Tilings
Emmanuel Jeandel (LIF), Pascal Vanier (LIF)

TL;DR
This paper investigates the slopes of periodic tilings, characterizing which slopes are possible and proving they correspond exactly to recursively enumerable sets of rationals.
Contribution
It provides a complete characterization of achievable slopes in tilings, showing they match recursively enumerable sets of rationals, a novel theoretical result.
Findings
Slopes of tilings are exactly the recursively enumerable sets of rationals.
The paper characterizes the set of slopes achievable with periodic tilings.
It establishes a correspondence between tiling slopes and computability theory.
Abstract
We study here slopes of periodicity of tilings. A tiling is of slope if it is periodic along direction but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they coincide with recursively enumerable sets of rationals.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics
