Abstract: Amorphic complexity - introduced by Fuhrmann, Gröger, and Jäger - is a relatively 
new invariant of topological dynamical systems useful in the study of aperiodic order (i.e. 
mathematical models of quasicrystals) and low complexity dynamics. Roughly speaking, 
finiteness of amorphic complexity corresponds to systems with discrete spectrum and 
continuous eigenvalues. We study amorphic complexity in the class of automatic systems - 
symbolic systems arising from constant length substitutions. We provide a closed formula 
for the amorphic complexity of any automatic system and show that tameness/nullness of such 
systems can be succinctly characterized through amorphic complexity: An infinite minimal 
automatic system is tame if and only if it is null if and only if its amorphic complexity 
is one. Our proof uses methods from fractal geometry and introduces some new dynamically-
defined pseudometrics. These methods seem suitable for study of other symbolic systems of 
S-adic nature including nonconstant length substitutions and Toeplitz subshifts. Time 
permitting we will touch on some possible generalisations in these directions. The talk 
is based on a joint work with Maik Gröger.