Abstract The design of multiagent simulations devoted to complex systems, addresses the issue of modeling behaviors that are involved at different space, time, behavior scales, each one being relevant so as to represent a feature of the phenomenon. We propose here a generic formalism intended to represent multiple environments, endowed with their own spatiotemporal scales and with behavioral rules for the agents they contain. An environment can be nested inside any agent, which itself is situated in one or more environments. This leads to a lattice decomposition of the global system, which appears to be necessary for an accurate design of multi-scale systems. This uniform representation of entities and behaviors at each abstraction level relies upon an interaction-oriented approach for the design of agent simulations, which clearly separates agents from interactions, from the modeling to the code. We also explain the implementation of our formalism within an existing interaction-based platform.