Overlapping substitutions and tilings
Overlapping substitutions and tilings
Inspired by \cite{DBZ},we generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. For such a substitution, the substitution matrix may have non-integer entries. We give the meaning of such a matrix by showing that the right Perron--Frobenius eigenvector gives the patch frequency of the resulting tiling. We also …