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Substitution sequences are sequences generated by successive applications of deterministic substitution rules on n letters that are, in general, neither regular nor disordered. We propose a simple algorithm for classifying uniform substitutions sequences concerning periodicity and/or almost periodicity, based only on the substitution rules, whose implementation was recently registered. That classification is based on two theorems – that are also proved – about almost periodicity (extended for non-uniform substitutions) and periodicity, respectively. It recognizes automatically the character of the sequences concerning the periodicity and almost periodicity: purely periodic, ultimately periodic, weakly non periodic, and strongly non-periodic. That recognization selects the non-periodic sequences; among them, it also selects automatically the ones that promote relevance of geometrical fluctuations on the critical behavior of spin models in relation to the homogeneous system . |
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