
IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Genetic CodeScript SourceBrown, Barton, et al. Dynamically Generated Hierarchies in Games of Competition. arXiv.1906.01383. By way of our philoSophia approach, Virginia Tech physicists and a Jacobs University, Bremen physicist (Hildegard MeyerOrtmanns) can be seen to achieve a quantified description of intrinsic natural “spontaneities” which evidently form on into complex, interactive, beneficial groupings. Spatial manyspecies predatorprey systems have been shown to yield very rich spacetime patterns. This observation begs the question whether there exist universal mechanisms for generating such emerging complex patterns in nonequilibrium systems. In this work we investigate the possibility of dynamically generated hierarchies in predatorprey systems. We analyze a ninespecies model with competing interactions and show that the situation results in the spontaneous formation of spirals within spirals. As cyclic interactions occur spontaneously in systems with competing strategies, the mechanism discussed in this work should contribute to our understanding of various social and biological systems. (Abstract excerpt) Brown, James and Geoffery West, eds. Scaling in Biology. New York: Oxford University Press, 2000. Papers from a Santa Fe Institute conference which explore the fractal and allometric scaling and selfsimilarity present in Metazoan anatomy and physiology, ecosystems and evolution. Life is amazing. Even the smallest bacterium is far more complex in its structure and function than any known physical system. The largest, most complex organisms, large mammals and giant trees, weigh more than 21 orders of magnitude more than the simplest microbes, yet they use basically the same molecular structures and biochemical pathways to sustain and reproduce themselves. (1) Brown, James, et al. The Fractal Nature of Nature: Power Laws, Ecological Complexity and Biodiversity. Philosophical Transactions of the Royal Society of London B. 357/619, 2002. Further insights into an intricate, tangled but knowable natural kingdom by virtue of its universally recurring principles. The Earth’s surface and the living things that inhabit it are incredibly diverse….Underlying this enormous physical and biological diversity, however, are emergent patterns that are precise, quantitative, and universal or nearly so. (619) Buchanan, Mark. Ubiquity: Why the World Is Simpler Than We Think. London: Weidenfeld & Nicolson, 2000. An accessible introduction to how the nonlinear sciences reveal a “universality” in nature and history. The same patterns and processes are in evidence from cosmic origins to world civilization and economic society because they spring from an independent dynamics of power laws and selforganized criticality. Cavalcante, Hugo, et al. Predictability and Control of Extreme Events in Complex Systems. arXiv:1301.0244. In this January 2013 posting, systems physicists Cavalcante and Marcos Oria, Universidade Federal da Paraiba, Brazil, Didier Sornette, ETH Zurich, and Daniel Gauthier, Duke University, provide further quantitative support for the theories of Sornette (search) and colleagues that warning signs of impending catastrophic calamities can in fact be limned from hypercomplexities such as climates and economies, contrary to many denials. These significance insights are also well explained by mathematician James Weatherall in his fine The Physics of Wall Street: A Brief History of Predicting the Unpredictable (Houghton Mifflin Harcourt, 2013) In many complex systems, large events are believed to follow powerlaw, scalefree probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme events. The mechanism responsible for the rare, largest events makes them distinct and their distribution deviates from a powerlaw. Based on this mechanism identification, we show that it is possible to forecast in real time an impending extreme event. Once forecasted, we also show that extreme events can be suppressed by applying tiny perturbations to the system. (Abstract)
Cepelewicz, Jordana.
The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal.
Quanta.
January 27,
2024.
A science reporter writew a luminous review about the whole history of such fractional theories from Benoit and his predecessors to their present state. Its focal occasion was a 2023 conference in Denmark to guide this now global project going forward. The article covers two main themes with vignettes of mathematicians who have spent lifetimes plumbing the endless depths of these equations. At the center are Misha Lyubich and Dima Dudko from SUNY Stony Brook whose years go back to Moscow, Ukraine and Belarus. We also meet Jeremy Kahn, Mitsuhiro Shishikura. Wolf Jung, Arnaud Chéritat of the University of Toulouse, Carsten Petersen of Roskilde University who chaired the meeting, Christophe Yoccoz, and more. The other half is a succinct tutorial all about fractal geometries with vivid graphs and images. Use a computer to zoom in on the Mandelbrot set’s jagged boundary, and you’ll encounter seahorses, parades of elephants, spiral galaxies and neuronlike filaments. No matter how deep you explore, you’ll always see nearcopies. That endless complexity was a core element of James Gleick’s 1987 book Chaos. The Mandelbrot set had become a symbol and represented the need for a new mathematical language, a better way to describe the fractal nature of the world. It illustrated how profound intricacy can emerge from the simplest of rules — much like life itself with relative order and disorder. (JC) Chandler, Jerry and Gertrudis Van de Vijver, eds. Closure: Emergent Organizations and Their Dynamics. New York: New York Academy of Sciences. Volume 901, 2000. Many articles consider autopoietic processes with regard to their property of constantly forming, describing and "closing" their “biosemiotic” identity. This is a signbased organic viability which pervades the natural realm as living systems refer to and enhance their own internal definition and individuality. Changizi, Mark and Darren He. Four Correlates of Complex Behavioral Networks: Differentiation, Behavior, Connectivity, and Compartmentalization. Complexity. 10/6, 2005. A hierarchical universality of these features is reported across a wide range of phenomena such as nervous systems, organisms, social groups, economies, and ecosystems. Chen, Yanguang. Zipf’s Law, l/f Noise, and Fractal Hierarchy. Chaos, Solitons, & Fractals. 45/1, 2012. As the extended Abstract conveys, a Peking University, College of Urban and Environmental Sciences, systems geographer contributes to the growing realizations of nature’s universally invariant, scalar repetition of the same structural and processual phenomena everywhere. Fractals, 1/f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/f spectrum is mathematically identical to Zipf’s law. Third, both 1/f spectra and Zipf’s law can be converted into a selfsimilar hierarchy. Fourth, fractals, 1/f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The selfsimilar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and ranksize distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems. (Abstract) Christensen, Kim and Nicholas Moloney. Complexity and Criticality. London: Imperial College Press, 2005. A technical work rooted in statistical mechanics that implies in part that selforganization in nonequilibrium systems may be a unifying concept for a emergent natural complexity. For our purposes, complexity refers to the repeated application of simple rules in systems with many degrees of freedom that gives rise to emergent behavior not encoded in the rules themselves. (vii) Criticality refers to the behavior of extended systems at a phase transition where observables are scale free, that is, no characteristic scales exist for these observables. (vii) Criticality is therefore a cooperative feature emerging from the repeated application of the microscopic laws of a system of interacting ‘parts.’ (vii) Chua, Leon. Local Activity is the Origin of Complexity. International Journal of Bifurcation and Chaos. 15/11, 2005. Another example of growing efforts to identify a common complex system, but with dense mathematics it is hard to see how this feature can fit the bill. But the universality concept – that the same complex dynamics recurs everywhere throughout a nested nature –has long been the payoff. Many scientists have struggled to uncover the elusive origin of “complexity,” and its many equivalent jargons, such as emergence, selforganization, synergetics, collective behaviors, nonequilibrium phenomena, etc…..The purpose of this paper is to show that all the jargons and issues cited above are mere manifestations of a new fundamental principle called local activity, which is mathematically precise and testable. (3435) Chua, Leon, et al. A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science. Part V: Fractals Everywhere. International Journal of Bifurcation and Chaos. 15/12, 2005. The other four parts appeared over the last two years in this publication. A highly technical meditation on a “universal computation” by cellular automata and neural networks which manifests a selfsimilarity throughout an emergent world.
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