Using bursting activity in two-dimensional (planar) neuronal cultures, we examine some constraints on biological computation. We are able to create reliable, mesoscale logical devices in vitro by geometrical axonal guidance. We control both the connections and activity by assembling living neural networks on quasi-one-dimensional configurations. The linear geometry yields reliable transmission lines. Incorporating thin lines creates 'threshold' devices and logical 'AND gates'. Breaking the symmetry of transmission makes neuronal 'diodes'. This approach to neuronal devices may contribute to the implementation of computation in vitro and, ultimately, to its understanding in vivo.