Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Shape convergence for aggregate tiles in conformal tilings


Authors: R. Kenyon and K. Stephenson
Journal: Proc. Amer. Math. Soc. 147 (2019), 4275-4287
MSC (2010): Primary 37F30; Secondary 05B45
DOI: https://doi.org/10.1090/proc/14453
Published electronically: June 27, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given a polygonal substitution tiling $ T$ of the plane with subdivision rule $ \tau $, we study the conformal tilings $ T_n$ associated with $ \tau ^nT$. We prove, under the assumption that there is somewhere a non-real similarity mapping one tile to another, that aggregate tiles within $ T_n$ converge in shape as $ n\rightarrow \infty $ to their associated Euclidean tiles in $ T$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37F30, 05B45

Retrieve articles in all journals with MSC (2010): 37F30, 05B45


Additional Information

R. Kenyon
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: rkenyon@math.brown.edu

K. Stephenson
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email: kstephe2@utk.edu

DOI: https://doi.org/10.1090/proc/14453
Received by editor(s): March 16, 2017
Received by editor(s) in revised form: October 30, 2017, and October 22, 2018
Published electronically: June 27, 2019
Additional Notes: Research of the first author was supported by NSF grants DMS-1612668, DMS-1713033 and the Simons Foundation award 327929.
Research of the second author was supported by Simons Foundation award 208523.
Communicated by: Ken Bromberg
Article copyright: © Copyright 2019 American Mathematical Society