Amorphic complexity is a relatively new invariant of dynamical systems useful in the study of aperiodic order and low complexity dynamics. Tameness is a well-studied notion defined in terms of the size of the Ellis semigroup of the system. In the talk we will study amorphic complexity and tameness in the class of automatic systems (systems arising from constant length substitutions). We will present a closed formula for the complexity of any automatic system and show that tameness of automatic systems can be succinctly characterised using amorphic complexity: an automatic system is tame if and only if its amorphic complexity is one. The talk is based on a joint work with Maik Gröger.