Composition of Composable Cellular Automata with respect to their dimensional attributes

The Composable Cellular Automata (CCA) specification, introduced in a previous article, formally defines a system for building cellular automata models that can be composed with other models. The purpose is to build hybrid simulation models of large, complex systems with uniquely modeled subsystems. Multiple subsystems of a hybrid model may implement the CCA specification. For the purposes of refining domain abstraction, reducing composition complexity, or improving model execution, these CCA may first be composed with each other to reduce the number of CCA models. A modeler must understand the impact that disparities between CCA may have on the potential composition. To that end, this paper builds upon the original publication to describe closure properties of formal composition of CCA with respect to their dimensional attributes-cell indices and time. From this, CCA can be composed and treated as a single CCA; thus reducing the overall complexity of the hybrid model.