Parallel evolutionary algorithms, over the past few years, have proven empirically worthwhile, but there seems to be a lack of understanding of their workings. In this paper we concentrate on cellular (fine-grained) models, our objectives being: (1) to introduce a suite of statistical measures, both at the genotypic and phenotypic levels, which are useful for analyzing the workings of cellular evolutionary algorithms; and (2) to demonstrate the application and utility of these measures on a specific example—the cellular programming evolutionary algorithm. The latter is used to evolve solutions to three distinct (hard) problems in the cellular-automata domain: density, synchronization, and random number generation. Applying our statistical measures, we are able to identify a number of trends common to all three problems (which may represent intrinsic properties of the algorithm itself, as well as a host of problem-specific features. We find that the evolutionary algorithm tends to undergo a number of phases which we are able to quantitatively delimit. The results obtained lead us to believe that the measures presented herein may prove useful in the general case of analyzing fine-grained evolutionary algorithms.