Complexity : a study of fractals and self-organized criticality (original) (raw)
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Fractal Fluctuations and Complexity: Current Debates and Future Challenges
Critical Reviews in Biomedical Engineering, 2012
Complexity is maybe one of the less understood concepts, even within the scientific community. Recent theoretical and experimental advances, however, based on the close relationship between the complexity of the system and the presence of 1/f fluctuations in its macroscopic behavior, have opened new domains of investigation, which consider fundamental questions as well as more applied perspectives. These approaches allow a better understanding of how essential macroscopic functions could emerge from complex interactive networks. In this review we present the current state of the theoretical debate about the origins of 1/f fluctuations, with a special focus on recent hypotheses that establish a direct link between complexity and fractal fluctuations, and clarify some lines of opposition, especially between idiosyncratic vs nomothetic conceptions, and global vs componential approaches. Finally, we discuss the deep questioning that this approach can generate with regard to current theories of motor control and psychological processes, and some future developments which may be evoked, especially in the domain of physical medicine and rehabilitation.
Complexity, contingency, and criticality
Proceedings of the National Academy of Sciences, 1995
Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or "punctuations" of all sizes. In the critical state, events which would otherwise be uncoupled become correlated. The apparent, historical corntingency in many sciences, including geology, biology, and economics, finds a natural interpretation as a self-organized critical phenomenon. These ideas are discussed in the context of simple mathematical models of sandpiles and biological evolution. Insights are gained not only from numerical simulations but also from rigorous mathematical analysis.
Metascience, 2005
This book is a serious and ambitious effort to explain how complex systems can exhibit simple behaviour. A complex system is any system having a sizable number of independent parts that occasionally interact. The parts are dubbed enions, to signify that the motion of each is predominantly independent of that of the others. Some examples of complex systems and their enions are a gas and its molecules, an ecosystem and its organisms, an economic system and its players. By contrast, a self-organising system (e.g., an embryo) is not complex in this sense since its parts are highly coordinated; they cannot be regarded as enions. Nor is a solid an enion, since each of its atoms constantly interacts with its nearest neighbors. It is less clear whether colloids and viscous liquids are complex; intermolecular forces play a sizable role in their micro-constituents. Only in gases do such forces typically play a small role.
Rapid self-organized criticality: Fractal evolution in extreme environments
Physical Review E, 2004
We introduce the phenomenon of rapid self-organized criticality (RSOC) and show that, like some models of self-organized criticality (SOC), RSOC generates scale-invariant event distributions and 1/f noise. Unlike SOC, however, RSOC persists despite more than an order of magnitude variation in driving rate and displays extremely thick and dynamic branching geometry. Starting with an initial set of parameter values, we perform two numerical experiments in which nonequilibrium RSOC systems are tuned towards their critical points. The approach to the critical state is tracked using average branching rates, which must equal 1 if systems are genuinely critical.
Complexity, bifurcation and chaos in natural and man-made lumped and distributed systems
Chemical Engineering Science, 2007
Complexity is a very diversified and branched subject and, ironically, is itself quite complex. In this paper, although we present the different aspects and definitions of complexity, we concentrate on its chemical/biological engineering relevance, especially for reaction/diffusion and hydrodynamic processes. System theory is used as the common language to unify concepts, and emphasis is given to bifurcation, chaos as the basis of behavioral complexity and the configuration of processes as the basis for structural complexity. Natural processes are grouped under biocomplexity, while man-made processes are treated as complexity alone. We restrict our attention in this paper to systems that do not change their structure during the process, so that self-organizational criticality is explained, but not utilized. Computational complexity is intrinsically inherent in all the processes we consider, but it is not given much attention in this paper. Despite these severe limitations on the scope of our paper, the subject is still quite complex and branched, and this paper tries to bring it to the attention and interest of a wider spectrum of chemical/biological engineers in both academia and industry.
Complexity theory and physical unification: From microscopic to macroscopic level
Chaos Theory: …, 2011
During the last two decades, low dimensional chaotic or selforganized criticality (SOC) processes have been observed by our group in many different physical systems such as space plasmas, the solar or the magnetospheric dynamics, the atmosphere, earthquakes, the brain activity as well as in informational systems. All these systems are complex systems living far from equilibrium with strong self-organization and phase transition character. The theoretical interpretation of these natural phenomena needs a deeper insight into the fundamentals of complexity theory. In this study, we try to give a synoptic description of complexity theory both at the microscopic and at the macroscopic level of the physical reality. Also, we propose that the self-organization observed macroscopically is a phenomenon that reveals the strong unifying character of the complex dynamics which includes thermodynamical and dynamical characteristics in all levels of the physical reality. From this point of view, macroscopical deterministic and stochastic processes are closely related to the microscopical chaos and self-organization. In this study the scientific work of scientists such as Wilson, Nicolis, Prigogine, Hooft, Nottale, El Naschie, Castro, Tsallis, Chang and others is used for the development of a unified physical comprehension of complex dynamics from the microscopic to the macroscopic level.
Toward a new “Fractals-General Science”
Alexandria Engineering Journal, 2014
A recent study has shown that everywhere real systems follow common ''fractals-general stacking behavior'' during their change pathways (or evolutionary life cycles). This fact leads to the emergence of the new discipline ''Fractals-General Science'' as a mother-discipline (and acting as upper umbrella) of existing natural and applied sciences to commonly handle their fractals-general change behavior. It is, therefore, the main targets of this short communication are to present the motives, objectives, relations with other existing sciences, and the development map of such new science. It is discussed that there are many foreseen illustrative applications in geology,