Emergent behaviour - system behaviour not determined by the behaviours of system components when considered in isolation - is commonplace in multi-agent systems, particularly when agents adapt to environmental change. This article considers the manner in which Formal Methods may be used to authenticate the trustworthiness of such systems. Techniques are considered for capturing emergent behaviour in the system specification and then the incremental refinement method is applied to justify design decisions embodied in the implementation. To demonstrate the approach, one and tw0-dimensional versions of Conway’s Game of Life are studied, and in particular an incremental refinement of ‘the glider’ is given from its specification.