  The apparent dichotomy between information-processing and dynamical
approaches to complexity science forces researchers to choose between two
diverging sets of tools and explanations, creating conflict and often hindering
scientific progress. Nonetheless, given the shared theoretical goals between
both approaches, it is reasonable to conjecture the existence of underlying
common signatures that capture interesting behaviour in both dynamical and
information-processing systems. Here we argue that a pragmatic use of
Integrated Information Theory (IIT), originally conceived in theoretical
neuroscience, can provide a potential unifying framework to study complexity in
general multivariate systems. Furthermore, by leveraging metrics put forward by
the integrated information decomposition ($\Phi$ID) framework, our results
reveal that integrated information can effectively capture surprisingly
heterogeneous signatures of complexity -- including metastability and
criticality in networks of coupled oscillators as well as distributed
computation and emergent stable particles in cellular automata -- without
relying on idiosyncratic, ad-hoc criteria. These results show how an agnostic
use of IIT can provide important steps towards bridging the gap between
informational and dynamical approaches to complex systems.
