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The Superconducting QUantum Interference Device (SQUID) is a highly nonlinearoscillator with rich dynamical behavior, including chaos. When driven by atime-periodic magnetic flux, the SQUID exhibits extreme multistability atfrequencies around the geometric resonance which is manifested by a"snake-like" form of the resonance curve. Repeating motifs of SQUIDs formmetamaterials, i. e. artificially structured media of weakly coupled discreteelements that exhibit extraordinary properties, e. g. negative diamagneticpermeability. We report on the emergent collective dynamics in two-dimensionallattices of coupled SQUID oscillators, which involves a rich menagerie ofspatio-temporal dynamics, including Turing-like patterns and chimera states.Using Fourier analysis we characterize these patterns and identifycharacteristic spatial and temporal periods. In the low coupling limit, theTuring-like patterns occur near the synchronization-desynchronizationtransition which can be related to the bifurcation scenarios of the singleSQUID. Chimeras emerge due to the multistability near the geometric resonance,and by varying the dc component of the external force we can make them appearand reappear and, also, control their location. A detailed analysis of theparameter space reveals the coexistence of Turing-like patterns and chimerastates in our model, as well as the ability to transform between these statesby varying the system parameters.

Pattern formation and chimera states in 2D SQUID metamaterials