2009/12/18 by Vivian Olsiewski Healey, Healey, Vivian Olsiewski
Engineering · Materials Science · Mathematics · Physics and Astronomy · #52C20 #52C23 #Advanced Materials and Mechanics #Advanced Mathematical Theories and Applications #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #math.MG #msc:52C20 #msc:52C23
paper · pdf · doi:10.48550/arxiv.0912.3814
24 pages, 31 figures
arxiv created 2009/12/18 · openalex publication_date 2009/12/18 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes a recomposition of the rhombic Penrose aperiodic protoset due to Robert Ammann. We show that the three prototiles that result from the recomposition form an aperiodic protoset in their own right without adjacency rules. An interation process is defined on the space of Ammann tilings that produces a new Ammann tiling from an existing one, and it is shown that this process runs in parallel to Penrose deflation. Furthermore, by characterizing Ammann tilings based on their corresponding Penrose tilings and the location of the added vertex that defines the recomposition process, we show that this process proceeds to a limit for the local geometry.