One of the most basic concepts in complexity science is self-organization. Self-organization is actually a concept that separates the attention and studies of chaos scientists from complexity scientists. In general, phase transformation of any non-linear system from simple to complex state (i.e. from order to chaos) is the main focus of the studies of scientists in the field of chaos theory, and vice versa, the transformation of any non-linear system from complex to The simple side (from chaos to order), which occurs mainly through the process of self-organization, is the main subject of studies of complexity scientists. Several definitions have been given for self-organization. The ability to create a structure, pattern or function without external interference is called self-organization for a system. In fact, the interaction of the components of a system at a lower level, which leads to the emergence of structure, properties and patterns at higher levels, is called self-organization. In general, it should be said that from the sub-cellular level to the level of large ecosystems in nature, the process of self-organization is established.
Self-organization can be seen in many phenomena of nature and social life of organisms. For example, if a large crowd of people has gathered in a sports field or an open-air music concert, we will encounter a chaotic crowd at the beginning, but after a while, the crowd will self-organize towards certain behavioral patterns and a kind of order emerges from the initial chaos.
The important thing here is that the collective movement of people in this example is not planned and implemented by a leader or manager, but the order created is the result of the interaction of people. The movement of schools of fish in the deep ocean, the flocks of birds, the collective movement of musicians in an orchestra and thousands of other examples can be said to be the result of the self-organization process.
If you put a container of water on a gas flame, after some time, hexagonal cells will form on the surface of the water and then the water will boil. The boiling of water is the result of positive and negative feedbacks that the hot layers at the bottom of the container and the upper cold layers impose on each other. In other words, to start the self-organization process, there is a need for positive and negative feedback between the constituent members of that system.
The specific formation and patterns governing the clouds in the sky are also based on the self-organization process. From the above examples, it can be concluded that self-organization occurs in conditions far from equilibrium (such as water heating). When a nonlinear system is in a state far from equilibrium, it can undergo a process of self-organization or self-motivated transformation and be drawn towards an order or a pattern of complex behaviors. Such bifurcations occur when the control parameters of a system are under the control of the system itself. This is another definition of self-organization. It is in this state that a chaotic system produces its form and state from internal guidelines and not from impositions imported from the outside world. The ability of self-organization in non-linear and chaotic systems is an inherent ability and does not require external interventions. Therefore, it can be said that chaos follows an orderly internal logic. But this order is completely different from the order mentioned in the mechanical representation of the world. In a mechanical world, order is created by unchangeable laws that can be understood through objective research, while in a chaotic world, order is an unstable combination of chance and plan (structure) with points of phase transformation and bifurcation in various directions. Infinite examples can be given for self-organization. Today, it is known that the way nerve cells of the brain are stimulated based on specific patterns, based on the self-organization process.
If we consider the Big Bang theory, existence is emerged by a self-organized process from the chaos caused by the explosion of the Big Bang. The process of human speech and uttering words is caused by patterns activated in the brain and the self-organization of these patterns with the tongue and muscles of the larynx and other involved organs. Another important point is that any kind of self-organization process occurs in the state of the system, which is dominated by a kind of “bounded instability”. That is, instability does not exist in the form of unlimited and chaos, but it is a kind of restriction on the ruling system. In the literature of complexity science, the state where a kind of bounded instability dominates the system is called the edge of chaos. For example, it is not possible to imagine that the members of an orchestra play any note they want, but a specific pattern or song should rule over all the activities of the members and the members of the band should organize themselves in the direction of that particular song. Today, even scientists seek to find self-organizing laws governing time and causality and believe that the governing laws of causality are self-organized by the way time flows.