The columnar organization is a ubiquitous feature in the cerebral cortex. In this study, a neural network model simulating the cortical columns has been constructed. When fed with random pulse input with constant rate, a column generates synchronized oscillations, with a frequency varying from 3 to 43 Hz depending on parameter values. The behavior of the model under periodic stimulation was studied and the input-output relationship was non-linear. When identical columns were sparsely interconnected, the column oscillator could be locked in synchrony. In a network composed of heterogeneous columns, the columns were organized by intrinsic properties and formed partially synchronized assemblies.