Abstract: We investigate sparse networks of threshold units, trained with the perceptron learning rule to act as associative memories. The units have position and are placed in a ring so that the wiring cost is a meaningful measure. A genetic algorithm is used to evolve networks that have efficient wiring, but also good functionality. It is shown that this is possible, and that the connection strategy used by the networks appears to maintain some connectivity at all distances, but with the probability of a connection decreasing rapidly with distance.