  Foam is a canonical example of disordered soft matter where local force
balance leads to the competition of many metastable configurations. Here we
present an experimental and theoretical framework for "active foam" where an
individual voxel inflates and deflates periodically. We explore structural
adaptations of this disordered material with respect to added activity.
Periodic injection of local activity leads to a small number of irreversible
and reversible T1 transitions throughout the foam. Regardless of the presence
of T1 transitions, individual vertices will displace outwards and subsequently
return back to their approximate original radial position; this radial
displacement follows an inverse law. Surprisingly, each return trajectory does
not retrace its outbound path but rather encloses a finite area, with either a
CW or CCW direction - which we define as a local swirl. These swirls form
coherent patterns spanning the entire scale of the material. Using a reduced
order dynamical model, we demonstrate that swirl arises as a direct consequence
of spatial disorder in the local micro-structure. Building a first principles
model, we demonstrate that disorder and strain rate control a crossover between
cooperation and competition between swirls in adjacent vertices. Over longer
timescales, the region around the active voxel structurally adapts from a
higher-energy metastable state to a lower energy state, indicative of a
localized annealing process. Finally, we develop a statistical toy-model that
evolves edge lengths based on a set of simple rules to explore how this class
of materials adapts over time as a function of initial structure. Adding
activity to foam couples structural disorder and adaptive dynamics to encourage
the development of a new class of abiotic, cellularized active matter.
