The spontaneous activity in the primary visual cortex (V1) of higher mammals shows spatially modular events of higher activity, where co-active regions are correlated to the underlying structure - orientation maps [1]. This activity travels in sparse waves, in line with the propagation speed of unmyelinated lateral connections [2]. Currently there is a lack of understanding of how these phenomena interact with each other and with evoked activity – so far, they have been only studied experimentally [1,4] and computationally [5,2] in isolation.We present a single large-scale spiking model of cat V1, which offers a unified computational theory of these phenomena. Our model exhibits spontaneous activity, travelling in sparse waves matching the conduction speed of V1 layer 2/3 horizontal connections, that is simultaneously correlated with the underlying orientation map. Additionally, stimulating the model with patterns congruent with the structured activity enhances its response.In addition to a wide variety of its previously reported [3] visual properties, our model demonstrates the compatibility of the identified mechanisms of spontaneous travelling waves and structured activity with the mechanisms required by the evoked regime.1. Smith, G.B. et al., M. Nat Neurosci 21, 1600–1608 (2018).2. Davis, Z.W. et al. Nat Commun 12, (2021).3. Antolík, J. et al., doi:10.1101/416156v5 (2023).4. Muller, L. et al., Nat Commun 5, (2014).5. Cai, D. et al., PNAS 102, 5868–5873 (2005)6. Mulholland, H.N. et al., doi:10.12751/NNCN.BC2021.P103 (2021).