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

2. 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

3. 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

4. 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

5. 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 2 1 0 z y x Distinguishes between internal and external I/O Specific mapping functions between cells and network as an entity