Reconstructability analysis (RA) is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss into lower ordinality relations. Set-theoretic RA (SRA) is used to characterize the mappings of elementary cellular automata. The decomposition possible for each mapping w/o loss is a better predictor than the λ parameter (Walker & Ashby, Langton) of chaos, & non-decomposable mappings tend to produce chaos. SRA yields not only the simplest lossless structure but also a vector of losses for all structures, indexed by parameter τ. These losses are analogous to transmissions in information-theoretic RA (IRA). IRA captures the same information as SRA, but allows the Walker-Ashby measures to be defined within its framework. The τ vector subsumes λ, Wuensche’s Z parameter, and Walker & Ashby’s fluency, memory, and hesitancy parameters within a single framework, and is a strong but still imperfect predictor of the dynamics. Of the parameters tested, fluency is the best scalar predictor of chaos.