Updown generation of Penrose patterns (Q753143)

Penrose's discovery of his infinite non-periodic tilings of the plane was based on the operation called deflation. Another more constructive way to generate the Penrose tilings discovered by J. Conway is the so-called updown generation which produces the infinite Penrose tilings by means of finite paths through a simple directed graph. The author establishes the connection between the two different ways to characterize the Penrose-tilings. A key to this is the dualization of the inflation - deflation idea.