Truchet Tilings and Renormalization
Dynamical Systems
2012-09-18 v3
Abstract
The Truchet tiles are a pair of square tiles decorated by arcs. When the tiles are pieced together to form a Truchet tiling, these arcs join to form a family of simple curves in the plane. We consider a family of probability measures on the space of Truchet tilings. Renormalization methods are used to investigate the probability that a curve in a Truchet tiling is closed.
Keywords
Cite
@article{arxiv.1103.6046,
title = {Truchet Tilings and Renormalization},
author = {W. Patrick Hooper},
journal= {arXiv preprint arXiv:1103.6046},
year = {2012}
}
Comments
34 pages, 11 figures. New version mentions the results of the paper: Gabor Pete, Corner percolation on Z^2 and the square root of 17. Annals of Probability 36 (2008), No. 5, 1711-1747. http://projecteuclid.org/euclid.aop/1221138764