External Editor: Kevin H. Knuth

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Self-organisation occurs in natural phenomena when a spontaneous increase in order is produced by the interactions of elements of a complex system. Thermodynamically, this increase must be offset by production of entropy which, broadly speaking, can be understood as a decrease in order. Ideally, self-organisation can be used to guide the system towards a desired regime or state, while “exporting” the entropy to the system’s exterior. Thus, Guided Self-Organisation (GSO) attempts to harness the order-inducing potential of self-organisation for specific purposes. Not surprisingly, general methods developed to study entropy can also be applied to guided self-organisation. This special issue covers a broad diversity of GSO approaches which can be classified in three categories: information theory, intelligent agents, and collective behavior. The proposals make another step towards a unifying theory of GSO which promises to impact numerous research fields.

Examples of self-organising systems can be found practically everywhere: a heated fluid forms regular convection patterns of Bénard cells, neuronal ensembles self-organise into complex spike patterns, a swarm changes its shape in response to an approaching predator, ecosystems develop spatial structures in order to deal with diminishing resources, and so on. One may ask whether it is possible to guide the process of self-organisation towards some desirable patterns and outcomes? Over the last decade, it has become apparent that this question can be rigorously formalised across multiple domains, leading to the emergence of a new research field: guided self-organisation (GSO) [

Guided self-organisation attempts to reconcile two seemingly opposing forces: one is guiding a self-organising system into a better structured shape and/or functionality, while the other is diversifying the options in an entropic exploration within the available search space. At first glance, these two alternatives may even appear irreconcilable in principle, given an apparent contradiction between the concepts of guidance (implying control) and self-organisation (implying autonomy). However, the resolution of this paradox capitalises on the distinction between the concepts of “control” and “constraint”: rather than trying to precisely control a transition towards the desirable outcomes, one puts in place some constraints on the system dynamics to mediate behaviors and interactions [

Intuitively, the imposed constraints guide the dynamics by reducing the bandwidth of relevant channel(s), so that the system progresses to preserve its information by self-improving and self-structuring. Here, information is understood in Shannon’s sense [

Some of the success on this path was underpinned by novelties in combining information-theoretic, graph-theoretic and computation-theoretic models, on the one side, with dynamical systems techniques and methods of statistical mechanics, on the other side. Fundamental connections between information-theoretic and thermodynamic (or statistical-mechanical) models reflect the rich common dynamics underlying guided self-organisation in open systems [

The mathematical study of graphs has had several advances in the last fifteen years into what is now described as “network science” [

Thus, it is not surprising that many studies of guided self-organisation turn their attention to the generic concepts of entropy and information, utilised in various thermodynamic, information-theoretic and graph-theoretic methods.

The 6th International Workshop on guided self-organisation was held in Barcelona on September 18, 2013, as a satellite Workshop at the 2013 European Conference on Complex Systems (ECCS’2013). Following the Workshop, a call for papers for a special issue on entropy methods in guided self-organisation was launched. Ten papers were selected after several rounds of comprehensive reviews.

The issue begins with three papers devoted to information-theoretical modelling of complexity and guided self-organisation.

The paper by Fuentes [

The study by Griffith

Ivancevic

The next three papers are devoted to applying information-theoretic models and tools to the generation of complex self-organising behaviors in intelligent agents.

As pointed out by Salge

The paper by Ristic

A novel internal control structure for a robot, considered as a general dynamic embodied system, is also investigated in the paper by Nurzaman

The next four papers apply information-theoretic, game-theoretic and graph-theoretic tools to studies of multi-agent collective behavior.

In the study carried out by Guckelsberger and Polani [

Harré and Bossomaier [

Gogolev and Marcenaro [

What is the optimal amount of entropy of a system? This question is explored by Zubillaga

The contributions to this special issue show that research on guided self-organisation is advancing along several theoretical and practical dimensions. The proposed formal theories and measures promise to bring us closer to a unifying theory of GSO with important implications for numerous research fields.

We would like to thank all of the reviewers for this special issue for their timely responses and useful comments. We are also grateful for the support provided by the organizers of the 2013 European Conference on Complex Systems (ECCS’2013) for facilitating the organisation of the GSO-2013 Workshop, as well as to our co-chair, Daniel Polani. We also appreciate the effort of all of the authors who submitted to the special issue and/or the GSO-2013.