Exploring Discrete Dynamics

Book Preface

Networks of sparsely inter-connected elements with discrete values and updating in parallel are central to a wide range of natural and artificial phenomena drawn from many areas of science: from physics to biology to cognition, to social science and economics; to parallel computation, emergence, self-organization and artificial life; to complex systems of all kinds.

Dynamics upon or on a network are its changing patterns of cell-states, while the network “architecture”, its connections and logic, remain fixed. DDLab studies these changing patterns and how they “fall” along trajectories into various attractors, revealing the fine detail of basins of attraction. DDLab also deploys flexible methods for constructing and changing the network’s architecture — the dynamics of the network — which of course has consequences for the dynamics on the network.

To give an oversimplified example, take a network of neurons in a brain; the pattern of firing and synaptic activity is the dynamics on the neural network sustaining automatic behavior, whereas network plasticity, changes in synaptic micro-circuitry and connections between neurons, is the dynamics of the network supporting learning and lifetime adaptation.

Networks like this are sometimes called “decision-making” because each element “decides” how to change based on the signals arriving from other elements along its input connections, mediated by its own internal logic, and each element provides outputs to other elements making their “decisions”. The many decisions make a collective by simultaneous iteration and massive feedback creating the possibility of all sorts of “emergent” dynamic patterns.