In this paper, after the introduction of the definition of State Controlled Cellular Neural Networks (SC-CNNs), it is shown that they are able to generate complex dynamics of circuits showing strange behaviour. Theoretical propoitions are presented to fix the templates of the SC-CNNs in such a way as to exactly match the dynamic behaviour of the circuits considered. The easy and cheap implementation of the proposed SC-CNN devices is illustrated and a gallery of experimentally obtained strange attractors are shown to confirm the practical suitability of the outlined strategy.