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Foam is a canonical example of disordered soft matter where local forcebalance leads to the competition of many metastable configurations. Here wepresent an experimental and theoretical framework for "active foam" where anindividual voxel inflates and deflates periodically. We explore structuraladaptations of this disordered material with respect to added activity.Periodic injection of local activity leads to a small number of irreversibleand reversible T1 transitions throughout the foam. Regardless of the presenceof T1 transitions, individual vertices will displace outwards and subsequentlyreturn back to their approximate original radial position; this radialdisplacement follows an inverse law. Surprisingly, each return trajectory doesnot retrace its outbound path but rather encloses a finite area, with either aCW or CCW direction - which we define as a local swirl. These swirls formcoherent patterns spanning the entire scale of the material. Using a reducedorder dynamical model, we demonstrate that swirl arises as a direct consequenceof spatial disorder in the local micro-structure. Building a first principlesmodel, we demonstrate that disorder and strain rate control a crossover betweencooperation and competition between swirls in adjacent vertices. Over longertimescales, the region around the active voxel structurally adapts from ahigher-energy metastable state to a lower energy state, indicative of alocalized annealing process. Finally, we develop a statistical toy-model thatevolves edge lengths based on a set of simple rules to explore how this classof materials adapts over time as a function of initial structure. Addingactivity to foam couples structural disorder and adaptive dynamics to encouragethe development of a new class of abiotic, cellularized active matter.

Active Foam: The Adaptive Mechanics of 2D Air-Liquid Foam under Cyclic Inflation