The magnetic and velocity field fluctuations in magnetohydrodynamic turbulence can be characterized by their directional alignment and induced electric field. These manifest as coherent spatial correlations which are measures of Alfvénicity and turbulence cascade strength, respectively. Solar wind observations and direct numerical simulations find that these distinctive correlations, caused by rapid relaxation processes that act to suppress nonlinearity, occur in localized spatial patches. This cellularization of magnetofluid turbulence is inconsistent with a superposition of Gaussian fields and could be related to spatial intermittency or other non-Gaussian statistics.