Complexity or Complex Systems Science is the generic term for the study of those multi-dimensional systems intermediate between the simple systems analyzable by Deterministic science and those vast ones whose study requires more Statistical scientific methods. In this realm we concentrate on the interactions or connections between the parts rather than on the parts themselves, collective or holistic non-reductionist models are thus used and these incorporate emergent hierarchical properties arising by Self-Organizational processes. This type of Complex Adaptive System is common in both biological and social areas, and they are increasingly also being found in inorganic realms, leading to a new interdisciplinary scientific methodology which has universal applicability for this class of system [for an popular overview see Lewin] and this viewpoint can also incorporate traditional scientific theories as special cases, with local constraints.
Due to the richness of such complex systems, many research directions can be taken, these include Genetic Algorithms (or more generally Evolutionary Computation) which concentrates on biological and optimisation concepts, Neural Networks which involve brain processes and learning, Iterated Function Systems (including L-Systems and Classifiers) which study developmental processes, Attractors which deal with self-organizing possibilities in state or phase space, Cellular Automata dealing with multicellular dynamics, Chaos or Nonlinear theory dealing with bifurcation and feedback, Fractals dealing with self-similarity and non-integer dimensions, and Artificial Life which concentrates on coevolution. All these areas employ a common collection of far-from-equilibrium complexity or connectionist concepts (with different emphases), including nonlinearity, causal loops, unpredictability, coevolution, fitness landscapes, emergence, phase changes and self-organized criticality. Much theoretical work has taken place around these concepts, which are now firmly established amongst the complexity community [e.g. Boden, Goodwin, Holland, Kauffman, Wolfram, Selected Online Complexity Papers and Books]. More in-depth information on complexity concepts and disciplines can be found in this series of Introductions.
In Artificial Life systems we take a collection of autonomous parts (called Agents) which can react to each other and can move between different internal states. These are created in an artificial computer world that supplies general resources and allows evolution to proceed in a discrete fashion (generation by generation). The purpose of this science is to study general life processes, or “Life as it could be” [Langton] - alternatives to life based upon DNA, as well as to gain a better understanding of our own planetary ecologies. There are many types of ALife experiments possible, using diverse computer models (and recently real-life robotics, games and internet bots also employ similar AI ideas) but in general terms an ALife agent comprises a genome or collection of characteristics which can mutate or change (using a Genetic Algorithm or similar) to provide evolutionary variation, the connections between the agents cause them to coevolve, self-organizing to create structures or functionality of some sort (similar to the more explicitly wired Neural Network learning system), the agents are generally mobile so transcend the fixed matrix used in Cellular Automata models, and they also incorporate a selective fitness measure (either explicit or implicit) that determines which agents survive or reproduce.
These sorts of systems settle into semi-stable emergent states, midway between a fully ordered static state and a structureless chaotic one (what is called 'Edge of Chaos', a 'Phase Transition' or 'Self-Organized Criticality') and these often show surprisingly lifelike behaviours (including predation, cooperation, parasitism and speciation). In general, many such attractor states are available (local optima - often equally fit) and systems tend to jump between these options in unpredictable ways, resembling the punctuated equilibria postulated by paleontologists and giving the power law distribution of perturbations seen also in many natural and social systems [Bak]. Many extensions to current Artificial Life work are still possible, including the incorporation of development and phenotypic emergence, the addition of learning (NN style) and richer, more realistic landscapes - ultimately perhaps leading to the creation of multi-level Artificial Organisms capable of existing in the real world. Current limitations on doing this are not theoretical but relate more to the highly computer intensive parallel processing necessary to model systems with sufficiently numerous and complex interacting agents, a problem which is rapidly becoming more tractable with computational developments.
Chris Lucas, February 2000