Self-Organizing Systems: A Tutorial in Complexity Ethan H. Decker
Department of Biology
University of New Mexico
Albuquerque, NM 87106, USA
Abstract: This is a tutorial on the processes and patterns of organization in complex natural systems. No technical details are included in describing the models or theories used. Instead, I focus on the concepts of self-organization, complexity, complex adaptive systems, criticality, the edge of chaos and evolution as they pertain to the formation of coherent pattern and structure in nature.
Introduction A burning question in physics, chemistry and biology is ``Where does order come from?'' Following the general laws of thermodynamics, physical and chemical systems follow the path of least resistance to dissipate any energy in the system. Eventually the system finds a low energy state, a dead calm, and remains at equilibrium there until some obvious perturbation increases its internal energy. For example, a pot of steaming sugar water will give off matter (water vapor) and energy (heat) until it reaches equilibrium with its environment. Cooling, evaporation and crystallization, governed by simple physical and chemical laws, will drive the system to a point of least energy, and the final resting state is rock candy in the bottom of a dry pot. The study of landscape ecology provides an example of how an SOS perspective differs from standard approaches. Ecologists are interested in how spatial and temporal patterns such as patches, boundaries, cycles, and succession arise in complex, heterogeneous communities. Early models of pattern formation use a `top-down' approach, meaning the parameters describe the higher hierarchical levels of the system. For instance, individual trees are not described explicitly, but patches of trees are. Or predators are modeled as a homogenous population that uniformly impacts a homogeneous prey population. In this way, the population dynamics are defined at the higher level of the population, rather than being the results of activity at the lower level of the individual.