  The Superconducting QUantum Interference Device (SQUID) is a highly nonlinear
oscillator with rich dynamical behavior, including chaos. When driven by a
time-periodic magnetic flux, the SQUID exhibits extreme multistability at
frequencies around the geometric resonance which is manifested by a
"snake-like" form of the resonance curve. Repeating motifs of SQUIDs form
metamaterials, i. e. artificially structured media of weakly coupled discrete
elements that exhibit extraordinary properties, e. g. negative diamagnetic
permeability. We report on the emergent collective dynamics in two-dimensional
lattices of coupled SQUID oscillators, which involves a rich menagerie of
spatio-temporal dynamics, including Turing-like patterns and chimera states.
Using Fourier analysis we characterize these patterns and identify
characteristic spatial and temporal periods. In the low coupling limit, the
Turing-like patterns occur near the synchronization-desynchronization
transition which can be related to the bifurcation scenarios of the single
SQUID. Chimeras emerge due to the multistability near the geometric resonance,
and by varying the dc component of the external force we can make them appear
and reappear and, also, control their location. A detailed analysis of the
parameter space reveals the coexistence of Turing-like patterns and chimera
states in our model, as well as the ability to transform between these states
by varying the system parameters.
