Events in self-timed rings can propagate evenly spaced or as bursts. By studying these phenomena, we obtain a better understanding of the underlying dynamics of self-timed pipelines, which is a necessary precursor to utilizing these dynamics to obtain higher performance. We show that standard bounded delay models are inadequate to discriminate between bursting and evenly spaced behaviours and show that an extension of the Charlie Diagrams of Ebergen, Fairbanks and Sutherland provides a framework for understanding these phenomena. This paper describes our novel analytical approaches and the design and fabrication of a chip to test our theoretical models.