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III. An Organic, Conducive, Habitable MultiUniVerse

F. 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. Self-Similar Models for the Mass Profiles of Early-Type Lens Galaxies. The Astrophysical Journal. 595/29, 2003. An example of how cosmologists are finding that scale-free 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 self-similarity 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 self-similarity.

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 Large-Scale 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, scale-free 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 large-scale organization of complex networks, both natural and artificial, has shown the existence of highly heterogeneous patterns of organization. Such patterns typically involve scale-free degree distributions and small-world, 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 scale-free 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 self-similar, 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 cross-sections 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 cross-sections through the lowest-loss 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 Two-degree Field Galaxy Redshift Survey. EPL. 85/29002, 2009. A team of Italian and Russian astronomers further quantify self-similar geometries across the celestial realms.

We apply the scale-length method to several three-dimensional samples of the Two-degree 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 large-scale 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 Kei-chi 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 scale-free structure during the evolution of the universe. (531)

Theel, Friethjof, et al. The Fractal Geometry of Hartree-Fock. Chaos. 27/12, 2017. When this section went online in 2004, scientific perceptions of a natural self-similarity 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 Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock 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 Hartree-Fock 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 λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well. (Abstract)

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