In the study of low-complexity aperiodic behaviour, tame and null systems arise naturally, yet providing concrete and easily testable conditions to establish their existence in a canonical class of systems is often nontrivial. In the talk I will present a recent result completely characterising tameness and nullness for minimal automatic systems generated by primitive constant-length substitutions in terms of a single numerical invariant: amorphic complexity, a topological invariant tailor-made to study zero-entropy systems with discrete spectrum. We show that for infinite automatic systems, tameness and nullness are equivalent to its value being one.

Preprint