Aperiodic structures and notions of order and disorder
Shelomo Izhaq Ben-Abraham, Alexander Quandt · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · 2010
The fabrication of artificial heterostructures is mainly based on substitution systems. We present simple ways to construct double-sided versions of the Fibonacci, Prouhet–Thue–Morse, paperfolding, period doubling and Golay–Rudin–Shapiro sequences. We also construct a generic instance of the two-dimensional Prouhet–Thue–Morse structure and explore its symbolic complexity. The complexity turns out to be polynomial and hence, the entropy goes to zero.