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.