Existing formal models of political behavior have followed the lead of the natural sciences and generally focused on methods that use continuous-variable mathematics. In 2002, Stephen Wolfram produced an extended critique of that approach in the natural sciences, and suggested that a great deal of natural behavior can be accounted for using rules that produce discrete patterns. This paper reports some initial findings designed to apply this pattern-based method to political event data. We believe that discrete sequence rule (DSR) models can provide a new social science methodology that is capable of preserving the agential basis of social interaction, tracking multiple agents as they enact rules through behavior directed at one another, and capturing the evolution of such interaction over time. The core of this project is a new, publicly accessible Web-based tool designed for the visualization and analysis of event data patterns (http://www.nkss.org). Using event data on the Israel–Palestine conflict generated by the TABARI automated coding program of the Kansas Event Data System (KEDS) for the period 1979–2004, we perform an initial exploration of this methodology. Specifically, we identify patterned behavior for which specific rule use can be imputed, and then examine several agent-based rules, plus four “meta-rules,” to parse Israeli–Palestinian interaction over time. Face validity of the analysis is apparent, and we also find the qualitative historical record can be augmented through observation of rule enactment in the event stream. Several descriptive empirical applications are demonstrated, including moving totals and increasingly complex sequences of rule enactment that go beyond the simple variations on tit-for-tat responses. While this paper represents an exploratory analysis of the method, the results are promising enough to warrant further investigation beyond its use in thick description as demonstrated here, to ultimately include hypothesis generation and falsification.