Truchet Tilings and Renormalization

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.

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

References in corpus (2)

• Corner percolation on ${\mathbb{Z}}^2$ and the square root of 17
• Renormalization of Polygon Exchange Maps arising from Corner Percolation

Cited by in corpus (2)

• The Triple Lattice PETs
• The Tetrahedral Twists