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This paper describes a recomposition of the rhombic Penrose aperiodicprotoset due to Robert Ammann. We show that the three prototiles that resultfrom the recomposition form an aperiodic protoset in their own right withoutadjacency rules. An interation process is defined on the space of Ammanntilings that produces a new Ammann tiling from an existing one, and it is shownthat this process runs in parallel to Penrose deflation. Furthermore, bycharacterizing Ammann tilings based on their corresponding Penrose tilings andthe location of the added vertex that defines the recomposition process, weshow that this process proceeds to a limit for the local geometry.

A Family of Recompositions of the Penrose Aperiodic Protoset and Its Dynamic Properties