Cortical spreading depression (CSD) along with migraine waves and spreading depolarization events with stroke or injures are the front-line examples of extreme physiological behaviors of the brain cortex which manifest themselves via the onset and spreading of localized areas of neuronal hyperactivity followed by their depression. While much is known about the physiological pathways involved, the dynamical mechanisms of the formation and evolution of complex spatiotemporal patterns during CSD are still poorly understood, in spite of the number of modeling studies that have been already performed. Recently we have proposed a relatively simple mathematical model of cortical spreading depression which counts the effects of neurovascular coupling and cerebral blood flow redistribution during CSD. In the present study, we address the main dynamical consequences of newly included pathways, namely, the changes in the formation and propagation speed of the CSD front and the pattern formation features in two dimensions. Our most notable finding is that the combination of vascular-mediated spatial coupling with local regulatory mechanisms results in the formation of stationary Turing-like patterns during a CSD event.