  The Weyl pseudo-metric is a shift-invariant pseudo-metric over the set of
infinite sequences, that enjoys interesting properties and is suitable for
studying the dynamics of cellular automata. It corresponds to the asymptotic
behavior of the Hamming distance on longer and longer subwords. In this paper
we characterize well-defined dill maps (which are a generalization of cellular
automata and substitutions) in the Weyl space and the sliding Feldman-Katok
space where the Hamming distance appearing in the Weyl pseudo-metrics is
replaced by the Levenshtein distance.
