
III. An Organic, Conducive, Habitable MultiUniVerseF. Systems Cosmology: Fractal SpaceTimeMatter Roukema, B. F., et al. A Hint of Poincare Dodecahedral Topology in the WMAP First Year Sky Map. Astronomy & Astrophysics. 423/821, 2004. Appropriately from the Nicolas Copernicus University in Torun, Poland, a further analysis of temperature fluctuations in the cosmic microwave background CMB as measured by the Wilkinson Microwave Anisotropy Probe WMAP satellite is seen to support the hypothesis that the overall universe is shaped as a dodecahedron rather than an infinite flat plane. Rusin, D., et al. SelfSimilar Models for the Mass Profiles of EarlyType Lens Galaxies. The Astrophysical Journal. 595/29, 2003. An example of how cosmologists are finding that scalefree power law profiles can describe the structure of the galactic clusters. Sanchez, Nestor and Emilio Alfaro. The Fractal Distribution of H II Regions in Disk Galaxies. Astrophysical Journal. 178/1, Supplement, 2008. “H II” means areas of interstellar hydrogen that is ionized, sans an electron. Instituto de Astrofísica de Andalucía astronomers here find these domains to likewise possess a constant fractal structure over galactic reaches. Sanchez, Nestor, et al. Fractal Dimension of Interstellar Clouds. Astrophysical Journal. 656/222, 2007. This conclusion is reached by studies of the opacity and noise of these celestial reaches. There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. (222) Slobodrian, R. Fractal Cosmogony. Chaos, Solitons and Fractals. 23/3, 2005. The structure of the early universe is noticed to exhibit a fractional selfsimilarity akin to microbial aggregates. Smet, Jurgen. Wheels within Wheels. Nature. 422/391, 2003. A report on the discovery that when electrons constrained to move in a plane are exposed to a perpendicular magnetic field, known as the Quantum Hall effect, the curve of voltage vs. field strength takes on an iterative, fractal selfsimilarity. Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic Books, 2001. Noted earlier in Quantum Cosmology, the work entertains theories of the grainy, fractal, and holographic character of an integral universe. We realized during that work that one way of making such a fractal spacetime is to build it up from a network of interacting loops. (124) Sole, Ricard and A. Munteanu. The LargeScale Organization of Chemical Reaction Networks in Astrophysics. EPL Europhysics Letters. 68/2, 2004. Universitat Pompeu, Fabra, Spain, systems theorists make an early, prescient notice that small world, scalefree topologies appear in astrochemical complexities. This reference is cited in a 2016 Nature Scientific Reports paper Multilayer Network Analysis of Nuclear Reactions (6/31882, 2016, see Liang Zhu in Systems Chemistry) whence a dozen years later this organic physiology and anatomy is robustly verified from cosmos to culture. The largescale organization of complex networks, both natural and artificial, has shown the existence of highly heterogeneous patterns of organization. Such patterns typically involve scalefree degree distributions and smallworld, modular architectures. One example is provided by chemical reaction networks, such as the metabolic pathways. The chemical reactions of the Earth's atmosphere have also been shown to give rise to a scalefree network. Here we present novel data analysis on the structure of several astrophysical networks including the chemistry of the planetary atmospheres and the interstellar medium. Our work reveals that Earth's atmosphere displays a hierarchical organization, close to the one observed in cellular webs. Instead, the other astrophysical reaction networks reveal a much simpler pattern consistent with an equilibrium state. (Abstract) Sroor, Hend, et al. Fractal Light from Lasers. arXiv:1809.02501. We cite this clever entry by University of Witwatersrand and CSIR National Laser Center, Pretoria, RSA researchers including Andrew Hughes for its quantified sense of how much our natural abide seems to be innately graced and suffused by selfsimilar, infinitely iterating geometries, which would quite please Galileo as we come upon 400 years of his famous avowal to this effect. Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished spherical mirrors, laser resonators are almost the precise opposite of Nature, and so it came as a surprise when, in 1998, transverse intensity crosssections of the eigenmodes of unstable canonical resonators were predicted to be fractals. Experimental verification has so far remained elusive. Here we observe a variety of fractal shapes in transverse intensity crosssections through the lowestloss eigenmodes of unstable canonical laser resonators, thereby demonstrating the controlled generation of fractal light inside a laser cavity. Our work offers a significant advance in the understanding of a fundamental symmetry of Nature as found in lasers. (Abstract) Sylos Labini, Francesco, et al. Persistent Fluctuations in the Distributions of Galaxies from the Twodegree Field Galaxy Redshift Survey. EPL. 85/29002, 2009. A team of Italian and Russian astronomers further quantify selfsimilar geometries across the celestial realms. We apply the scalelength method to several threedimensional samples of the Twodegree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies controlling systematic effects. By determining the probability density function of conditional fluctuations we show that largescale structures are quite typical and correspond to large fluctuations in the galaxy density field. We do not find a convergence to homogeneity up to the samples sizes, i.e. 75 Mpc/h. We then measure, at scales r Tatekawa, Takayuki and Keichi Maeda. Primordial Fractal Density Perturbations and Structure Formation in the Universe. The Astrophysical Journal. 547/531, 2001. A technical paper on how such recurrently ordered forms appear and ramify in the developing cosmos. One of the most plausible explanations is the nonlinear dynamics of the perturbations will provide such a scalefree structure during the evolution of the universe. (531) Theel, Friethjof, et al. The Fractal Geometry of HartreeFock. Chaos. 27/12, 2017. When this section went online in 2004, scientific perceptions of a natural selfsimilarity from atomic depths to cosmic breadth were spurious and rudimentary, with a smattering of evidence. A decade and a half later, as this entry by University of Hamburg physicists, and many citations herein now testify, iterative fractal forms are quantified and known to array across these reaches, and everywhere in between. Circa 2018, by a natural philosophy view, our worldwide humankinder seems to be well finding a new genesis universe graced by these intrinsic phenomenal qualities. OK The HartreeFock method is an important approximation for the groundstate electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The HartreeFock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the HartreeFock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λplane, which resemble the wellknown Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well. (Abstract)
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