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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.