Book excerpt: EXPLORING DISCRETE DYNAMICS is a comprehensive guide to studying cellular automata and discrete dynamical networks with the classic software Discrete Dynamics Laboratory (DDLab). These collective networks are at the core of complexity and emergent self-organisation. With interactive graphics, DDLab is able to explore an huge diversity of behaviour -- mostly terra incognita -- space-time patters, but also basins of attraction, mathematical objects representing the convergent flow in state-space. Applications range within physics, mathematics, biology, cognition, society, economics and computation, and more specifically in neural and genetic networks, artificial life, and a theory of memory.