Modelling non-periodic systems by binary uniform substitution sequences

Substitution sequences are used for modelling non-homogeneous interactions between elements (atoms, spins, etc.) that form up neither periodic nor disordered lattice models whose physical properties may be different from those of homogeneous systems. In this work, we present a classification of substitution sequences generated by 2-letters uniform rules concerning periodicity with its demonstration as well as its relation with the concept of almost periodicity. We also discuss some physical consequences of our classification regarding spin models.