Discrete models of continuous behavior of collective adaptive systems

Artificial ants are "small" units, moving autonomously on a shared, dynamically changing "space", directly or indirectly exchanging some kind of information. Artificial ants are frequently conceived as a paradigm for collective adaptive systems. In this paper, we discuss means to represent continuous moves of "ants" in discrete models. More generally, we challenge the role of the notion of "time" in artificial ant systems and models. We suggest a modeling framework that structures behavior along causal dependencies, and not along temporal relations. We present all arguments by help of a simple example. As a modeling framework we employ Heraklit; an emerging framework that already has proven its worth in many contexts.