<p>Periodic potentials have been widely used to control the phase behavior of colloidal suspensions in equilibrium, particularly to induce freezing and melting phase transitions. Recently, much progress has also been made in controlling the phases of active colloids that can self-propel and are far from equilibrium. While some recent studies have explored controlling active colloids using periodic potentials, the majority of research has focused on spatially uniform fields. Here we transfer the concept of lattice-induced freezing and melting to active systems and show that imposing a spatially periodic potential on active colloids not only triggers freezing and melting transitions but additionally leads to the emergence of a so-far unknown active matter phase. This phase, which we term “active adaptolates”, adopts the geometry of the underlying lattice like a frozen phase, forms an interconnected percolated structure, and maintains the ballistic dynamics of the molten phase. These results demonstrate the potential to use external patterned fields to design the internal structure of active systems without disrupting their intrinsic dynamics.</p>