The design and implementation of synthetic gene regulatory networks that compute is a central effort to synthetic biology. Genetic components are arranged into circuits to perform pre-defined functions such as logic gates or bistable switches in living cells. Despite the success of the field there is vast room for improvements since the mechanistic workings of living systems are still largely unknown. For example, the implementation of synthetic circuits often follows topological rules from engineering, with genetic gates arranged one after the other to mimic an electronic circuit. However, natural regulatory networks have evolved architectures full of feedbacks, redundancies and unexpected or counter-intuitive (to us) connections. Here, we computationally explore that search space of topological arrangements for synthetic networks. We fix circuit parameters, define output dynamics, and use an evolutionary algorithm based on Cartesian Genetic Programming to evolve solutions that can be realised as synthetic gene networks. Results suggest there are emergent properties hidden in counter-intuitive implementations that impact decisively on phenotypic responses—an aspect so far neglected. We use stochastic simulations to measure the results against both human designed networks, and use the design of a genetic inverter and the design of a genetic AND gate as example problems.