Towards an extensible calculus for spatial computation

Spatial computing is the study of distributed systems in which the position in space of each node has a direct impact on the computation that that node carries out. Related areas include swarm intelligence, amorphous computing, and autonomous multi-agent systems. We present our preliminary efforts at implementing a general purpose simulation toolkit for researching spatial computing. Our toolkit centers around the locality principle that at any time, the computation occurring on a node is determined only by the program it started with and the data in its immediate vicinity (i.e. the sensory data at the node's location and the logical data communicated to it by its direct neighbours). We do not presume identical capabilities for all nodes, nor does the toolkit insist on any particular models of computation and communication for the system; rather, we leave the specification of those models up to the researcher using the toolkit. Facilitating these degrees of freedom, while retaining control over the essential elements of a maximally parallel simulation of the distributed system is what sets our toolkit apart from others similar to it, such as Swarm [1], TOSSIM [2] and MASON [3]. To demonstrate the plausibility of our toolkit, we present how it would be used to implement a simulation of a simple canonical problem of spatial computing - that of establishing a gradient field. We also discuss how it would be used to explore other spatial computing problems.