The key idea in this paper is to computationally model situations where emergence of this particular sort can happen. It will take some work to get there, however. Section \ref{sec:literature-review} develops 13 key criteria for the evaluation of serendipity based on a review of several well-known examples of serendipitous discoveries from human history. Section \ref{sec:foundations} describes a working testbed for exploring serendipitous computational discovery. In Section \ref{sec:patterns-of-serendipity}, we apply our 13 criteria to analyse several narrative “patterns of serendipity” collected by van Andel \cite{van1994anatomy}. Section \ref{sec:patterns-of-serendipity} is the theoretical core of the paper; here we give our interpretation of the design pattern methodology. In Section \ref{sec:computational-serendipity}, we focus on serendipity in a computational context, condensing our criteria into an operational definition, making our treatment of design patterns more concrete, and proposing an experimental setup that we think will exhibit many of the relevant features. In Section \ref{sec:related}, we examine related work, and in Section \ref{sec:recommendations}, we advance our recommendations for researchers working on computational creativity (and serendipity).