A Composable Discrete-Time Cellular Automaton Formalism Gary R. Mayer Hessam S. Sarjoughian Arizona Center for Integrative Modeling & Simulation SBP ’08 01 April 2008 Phoenix, Arizona

Rationale Cellular Automata has a central role in simulating many physical systems such as landscape processes Interesting complex systems can be best described using CA and other kinds of models Example: sustainable socio-ecological organizations

CA Approaches CA is intuitive for representing processes that can be cast into uniform structure with varied behavior – e.g., land surface erosion CA is used to represent non-cellular abstractions – e.g., restrictive for agent decision making CA is often combined with other models using arbitrary data and control schemes – e.g., programming languages Existing CA formalisms treat CA as a grey box Initialize and peek at current state

Composable CA Composable CA extends the CA formalism to formally represent non-cellular model interactions Benefits Avoid ambiguous composition of CAs with other models through formal description of I/O relationships Improve hybrid modeling for CA models Support detailed representations of agent and landscape process interactions Simplify model verification and simulation validation Model interaction visibility

Composable CA Specification Represented as a network, N, of cells (individual automata) N =  X N, Y N, D, {M ijk }, T, F , where M ijk =  X ijk, Y ijk, Q ijk, I ijk,  ijk, ijk, T  F = { f in, f out } Difference between multi-dimensional CA and two composed CCAs is in the mapping z y x Distinguishes between internal and external I/O Specific mapping functions between cells and network as an entity