Self-Organization: Definitions & Main Ingredients

Various definitions of self-organization have been proposed (arranged chronologically below):

table 01

Self-organization is considered as:
[01]. Indicative of a machine that is "determinate and yet able to undergo spontaneous changes of internal organization."
[02]. "A set of dynamical mechanisms whereby structures appear at the global level of a system from interactions among its lower level components."
[03]. "Associated with the spontaneous emergence of long-range spatial and/or temporal coherence among the variables of the (organized) system."
[04]. "The spontaneous emergence of coherence or structure without externally applied coercion or control.".
[05]. "A system is self-organizing if it acquires a spatial, temporal or functional structure without specific interference from the outside."
[06]. "The ability of systems comprising many units and subject to constraints, to organized themselves in various spatial, temporal or spatio-temporal activities. These emerging properties are pertinent to the system as a whole and cannot be seen in units which comprise the system."
[07]. "The creation of macroscopic patterns by the action of forces distributed in a much more homogeneous way than the structures that arise. Hence, this kind of transformation implies a spontaneous breaking of symmetry."
[08]. "The spontaneous emergence of nonequilibrium structural organization on a macroscopic level due to collective interactions between a large number of simple, usually microscopic, objects."
[09]. "A process where the organization (constraint, redundancy) of a system spontaneously increases, i.e. without this increase being controlled by the environment or an encompassing or otherwise external system."
[10]. "A process in which pattern at the global level of a system emerge solely from numerous interactions among the lower-level components of the system. Moreover, the rules specifying interactions among the system’s components are executed using only local information, without reference to the global pattern."
[11]. "Self-organization" is a concept described in many disciplines, particularly in physics and biology, it’s a phenomenon whereby system-level patterns spontaneously arise solely from interactions among subunits of the system.
[12]. "The evolution of a system into an organized form in the absence of external constraints."
[13]. "The introduction of correlations (patterns) over time or space for previously independent variables operating under local rules."
[14]. "It describes how microscopic processes cause macroscopic patterns in nonequilibrium systems."

    These definitions are equivalent, the 12th being the most intuitive. Simply put, a system is self-organizing if it doesn’t require any external force to self-organize.

    Two terms must be precised for a deep comprehension, "pattern" and "emergence"; The word pattern is applied to an organized arrangement of objects in space or time. An emergent property on the other hand is a characteristic that appears unexpectedly (without being explicitly determined) from interactions among the components of the system. We thus will speak of emergence to underline the undetermined character of a property without referring that this property is organized in structure, or placed at a different interactions level.

    What is also crucial is the existence of multiple low-level components and therefore multiple interactions, or probably even a sole individual but multiple repeated interactions (transitory phases often take place like the emergence of patterns is produced solely under a certain critical number or a density of interactions or components). Also, table 01 proves that the authors of these definitions consider that global level properties must come only from within the system, they are not thus generated on the basis of an interference of other external leading forces. Yet this doesn’t mean that the environment doesn’t play any role. In fact, self-organized systems exhibit often what is  designated by the term : "multistability", so that the system can opt among different semi-stable structures, though without changing the low-level behavioral characteristics. More importantly, the system can opt according to intrinsic factors, like random fluctuations within the system, or extrinsic factors such as the little changes in the environment with which the system interacts.

The main question consequently is to understand how the components of a system interact among each other to produce a complex pattern (with the relative sense of the term, i.e., more complex than the components themselves). Four necessary ingredients and three characteristics are identified.

(1) .  The principal ingredients of self-organization:

1. Positive feedback: As one of the driving change in the system (usually nonstabilizing change, that is, change in the same direction as a perturbation. This mechanism denote a set of simple behavioral 'rules of thumb' that promote the creation of structures. Examples of positive feedback include recruitment and reinforcement. For instance, recruitment to a food source is a positive feedback that relies on trail laying and trail following in some ant species, and dances in bees.
2. Negative feedback: Negative feedback counterbalances positive feedback and helps to stablize the collective pattern (so it's a stablizing force), it may take the form of saturation, exhaustion or competition. In the example of foraging ants cited in section 03, when satiation happened or that the source is drained, a loop of negative feedback takes place; a mechanism that reduced itself. If we consider the traces of pheromone evaporating rapidly, once the food source is dried up, lesser and lesser ants tend to follow the trace which will ends by disappearing.
3. Amplification of fluctuations: Stochasticity and randomness generating diversion upon which the feedback works. E.g. random walks, errors, random task switching, etc. Not only do structures emerge despite randomness, but randomness is often crucial, since it enables the discovery of new solutions, and fluctuations can act as seeds from which structures nucleate and grow.
4. Multiple interactions: All cases of self-organization rely on multiple interactions. A single individual can generate a self-organized structure such as a trail provided pheromonal lifetime is sufficient, self-organization generally requires a minimal density of mutually tolerant  individuals. Moreover, individuals should be able to make use of the results of their own activities as well as of others' activities (although they may perceive the difference): For  instance, trail networks can self-organize and be used collectively if individuals use others' pheromone. This does not exclude the existence of individual chemical signatures or individual memory which can efficiently complement or sometimes replace responses to collective marks.

(2) .  The characteristic signatures of self-organization include:

1. The creation of spatiotemporal structures in an initially homogeneous medium. 
2. Multistability:  The possible coexistence of several stable states; Because structures emerge by amplification of random deviations (Like even only the little modifications in the individual behavior can lead to a big change in the collective behavior (we say also multi-stationarity ). And the little modifications in the environment, without touching the individual behavior, can lead to different collective states), any such deviation can be amplified and the system converges to one among several possible stable states, depending on initial conditions.
3. The existence of bifurcations when some parameters are varied and Symmetry breaking: Very often a self-organizing system will have more than one stable organized state, or attractor. While moving from the initial, disorganized state, the system must make some "decision" as to which organized state it will seek (these decisions typically being made by random differences or perturbations in the initial state). These decision points are called "bifurcations" and are a form of symmetry breaking.