In this paper, we demonstrate how behavioural structure, such as a finite state machine, can emerge in minimal robots without computation nor memory capabilities. As a case study we observe the ability of a group of non-holonomic robots to form robust, self-healing circle formations in a decentralized manner using only a limited frontal binary sensor. We present a grid-search method to find suitable parameters that promote the formation of a stable circle. We then examine how the parameters of the controllers affect the appearance of the behaviour, and provide theoretical proof for its emergence and self-healing properties. We validate the proposed model through a set of experiments with ten mobile real robots. Our results with real robots match the simulated experiments and provide insights on how a simple, computation-free behaviour can generate complex spatio-temporal dynamics.