On Systems: On Self-Organization (2010-)

"In the telephone system a century ago, messages dispersed across the network in a pattern that mathematicians associate with randomness. But in the last decade, the flow of bits has become statistically more similar to the patterns found in self-organized systems. For one thing, the global network exhibits self-similarity, also known as a fractal pattern. We see this kind of fractal pattern in the way the jagged outline of tree branches look similar no matter whether we look at them up close or far away. Today messages disperse through the global telecommunications system in the fractal pattern of self-organization." (Kevin Kelly, "What Technology Wants", 2010)

"Most systems in nature are inherently nonlinear and can only be described by nonlinear equations, which are difficult to solve in a closed form. Non-linear systems give rise to interesting phenomena such as chaos, complexity, emergence and self-organization. One of the characteristics of non-linear systems is that a small change in the initial conditions can give rise to complex and significant changes throughout the system. This property of a non-linear system such as the weather is known as the butterfly effect where it is purported that a butterfly flapping its wings in Japan can give rise to a tornado in Kansas. This unpredictable behaviour of nonlinear dynamical systems, i.e. its extreme sensitivity to initial conditions, seems to be random and is therefore referred to as chaos. This chaotic and seemingly random behaviour occurs for non-linear deterministic system in which effects can be linked to causes but cannot be predicted ahead of time." (Robert K Logan, "The Poetry of Physics and The Physics of Poetry", 2010)

"Nature is capable of building complex structures by processes of self-organization; simplicity begets complexity." (Victor J Stenger, God: "The Failed Hypothesis", 2010)

"But one of the major findings of quantum theory is the recognition that the universe is an open system. Open systems are neg-entropic (-S) and exhibit a tendency toward order. This means that according to quantum theory, the universe is a self-organizing system, continuously expanding and moving toward increasing order and complexity. In this context even subatomic particles show open system behavior and self-referencing tendencies." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"A self–organizing system acts autonomously, as if the interconnecting components had a single mind. And as these components spontaneously march to the beat of their own drummer, they organize, adapt, and evolve toward a greater complexity than one would ever expect by just looking at the parts by themselves." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Complex systems are networks made of a number of components that interact with each other, typically in a nonlinear fashion. Complex systems may arise and evolve through self-organization, such that they are neither completely regular nor completely random, permitting the development of emergent behavior at macroscopic scales." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

"There are several reasons why reaction-diffusion systems have been a popular choice among mathematical modelers of spatio-temporal phenomena. First, their clear separation between non-spatial and spatial dynamics makes the modeling and simulation tasks really easy. Second, limiting the spatial movement to only diffusion makes it quite straightforward to expand any existing non-spatial dynamical models into spatially distributed ones. Third, the particular structure of reaction-diffusion equations provides aneasy shortcut in the stability analysis (to be discussed in the next chapter). And finally, despite the simplicity of their mathematical form, reaction-diffusion systems can show strikingly rich, complex spatio-temporal dynamics. Because of these properties, reaction-diffusion systems have been used extensively for modeling self-organization of spatial patterns." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

"Without chaos there would be no creation, no structure and no existence. After all, order is merely the repetition of patterns; chaos is the process that establishes those patterns. Without this creative self-organizing force, the universe would be devoid of biological life, the birth of stars and galaxies - everything we have come to know. (Lawrence K Samuels, "Chaos Gets a Bad Rap: Importance of Chaology to Liberty", 2015)

"Cybernetics studies the concepts of control and communication in living organisms, machines and organizations including self-organization. It focuses on how a (digital, mechanical or biological) system processes information, responds to it and changes or being changed for better functioning (including control and communication)." (Dmitry A Novikov, "Cybernetics 2.0", 2016)