The term serendipity describes a creative process that develops, in context, with the active participation of a creative agent, but not entirely within that agent's control. While a system cannot be made to perform serendipitously on demand, we argue that its $\mathit{serendipity\ potential}$ can be increased by means of a suitable system architecture and other design choices. We distil a unified description of serendipitous occurrences from historical theorisations of serendipity and creativity. This takes the form of a framework with six phases: $\mathit{perception}$, $\mathit{attention}$, $\mathit{interest}$, $\mathit{explanation}$, $\mathit{bridge}$, and $\mathit{valuation}$. We then use this framework to organise a survey of literature in cognitive science, philosophy, and computing, which yields practical definitions of the six phases, along with heuristics for implementation. We use the resulting model to evaluate the serendipity potential of four existing systems developed by others, and two systems previously developed by two of the authors. Most existing research that considers serendipity in a computing context deals with serendipity as a service; here we relate theories of serendipity to the development of autonomous systems and computational creativity practice. We argue that serendipity is not teleologically blind, and outline representative directions for future applications of our model. We conclude that it is feasible to equip computational systems with the potential for serendipity, and that this could be beneficial in varied computational creativity/AI applications, particularly those designed to operate responsively in real-world contexts.
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