III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Incubator Lifescape

E. Systems Cosmology: Fractal SpaceTimeMatter

Jarboe, Thomas, et al. Self-Organization of Solar Magnetic Fields. arXiv:1807.09593. We cite this entry by nine University of Washington astrophysicists for its content, and also to make a point, which ought to be strongly put, that these formative stellar forces come from the same natural, independent source as those which organize life’s origin, cellular activities, our brains and linguistic societies. They strongly imply, as this universality becomes filled in, a single, common program, aka a uniVerse to human epitome cosmome code.

Self-organization properties of sustained magnetized plasma are applied to solar data to understand solar magnetic fields. Torsional oscillations are speed-up and slow-down bands of the azimuthal flow that correlate with the solar cycle, and they imply the existence of a symmetric solar dynamo. The dynamo has enough power to heat the chromosphere and to power the corona and the solar wind. (Abstract brief)

Jones, Bernard, et al. Scaling Laws in the Distribution of Galaxies. Reviews of Modern Physics. 76/4, 2004. An extensive technical paper with co-authors Vicent Martinez, Enn Saar and Virginia Trimble. The phenomenon of a worldwide humankind explores and discovers an inherently variegated, clustered, self-similar universe from which it arose.

In describing scaling laws it is helpful to make analogies with fractals, mathematical constructs that can possess a wide variety of scaling properties. We must beware, however, of saying that the universe is a fractal on some range of scales: it merely exhibits a specific kind of fractal-like behavior on those scales. The richness of fractal scaling behavior is an important supplement to the usual battery of statistical descriptors. (Abstract, 1211) The aim of this article is to show how the paradigm of a homogeneous and isotropic universe with a hot singular origin has emerged, and to explain how, within this framework, we can quantify and understand the growth of the large scale cosmic structure. (1213) This scaling is almost certainly a consequence of two factors: the nature of the initial conditions for cosmic structure formation and the fact that the gravitational force law is itself scale-free. (1215)

Kempkes, Sander, et al. Design and Characterization of Electrons in a Fractal Geometry. Nature Physics. 17/2, 2019. As the Abstract details, Utrecht University physicists deftly show how even atoms and electrons, in their dynamic forms, naturally take on this iterative patterning. We offer two comments. When this section was first posted in 2004, the presence of a common, natural self-similarity was spurious and patchy. Fifteen years later it has become robustly evident that every universal, atomic, and animate complexity is graced by this infinite iteration. Whomever in the cosmos are we peoples to consider and begin a second materiality by way of “artificial atoms.” See also in the same issue Quantum Fractals by Dario Bercioux and Ainhoa Iriguez.

Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu (111) surface, and how these sites couple to form electronic Sierpiński fractals. We characterize the electron wavefunctions at different energies with scanning tunnelling microscopy and spectroscopy, and show that they inherit the fractional dimension. Wavefunctions delocalized over the Sierpiński structure decompose into self-similar parts at higher energy, and this scale invariance can also be retrieved in reciprocal space. Our results show that electronic quantum fractals can be artificially created by atomic manipulation in a scanning tunnelling microscope. Moreover, the rational concept of artificial atoms can readily be transferred to planar semiconductor electronics, allowing for the exploration of electrons in a well-defined fractal geometry, including interactions and external fields. (Abstract)

Krioukov, Dmitri, et al. Network Cosmology. Nature Scientific Reports. 2/793, November, 2012. On occasion, a paper comes along of such unique, meritous content that it bodes for a significant breakthrough and synthesis. A team of five University of California, San Diego, systems scientists with Marian Boguna, a University of Barcelona physicist, proceed via sophisticated quantifications to discern the same nonlinear dynamics that infuse from proteins to cities within celestial topological networks. Its technical acumen and depth requires several excerpts. For example, Figure 2, “Mapping between the de Sitter universe and complex networks” illustrates many isomorphic affinities. As per Figure 4, “Degree distribution and clustering in complex networks and space time,” Internet, social network, brain anatomy, and hyperbolic spatial lineaments all graph on the same line, indicating common node and link geometries. As the quotes allude, a grand unification of universe, life, cognition, and humankind could be in the offing, a nascent witness of a biological genesis uniVerse.

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology. (Abstract)

Physics explains complex phenomena in nature by reducing them to an interplay of simple fundamental laws. This very successful tradition seems to experience certain difficulties in application to complex systems in general, and to complex networks in particular, where it remains unclear if there exist some unique universal laws explaining a variety of structural and dynamical similarities found in many different real networks. One could potentially remedy this situation by identifying a well-understood physical system whose large-scale dynamics would be asymptotically identical to the dynamics of complex networks. One could then try to use the extensively studied dynamical laws of that physical system to predict and possibly control the dynamics of networks. (1)

We show here that there exists a very simple but completely unexpected connection between networks and cosmology. In cosmology, de Sitter spacetime plays a central role as the exact solution of Einstein’s equations for an empty universe, to which our universe asymptotically converges. Here we show that graphs encoding the large-scale causal structure of de Sitter spacetime and our universe have structure common to many complex networks, and that the large-scale growth dynamics of these causal graphs and complex networks are asymptotically the same. (1)

In short, past light cones of new nodes, shown by green in Fig. 2, are asymptotically equal to the corresponding hyperbolic discs, shown by red. The green light cone bounds the set of nodes to which node P connects as a new causet element. The red hyperbolic disc bounds the set of nodes to which P connects as a new node in the hyperbolic network model that accurately describes the growth of real networks. Since these two sets are asymptotically the same, we conclude that not only the structure, but also the growth dynamics of complex networks and de Sitter causets are asymptotically identical. (5)

Kroger, Helmut, ed. Fractal Geometry in Quantum Physics. Chaos, Solitons & Fractals. 14/6, 2002. A special issue to explore the pervasive self-similarity of nature from sub-atomic to galactic realms.

Landais, Francois, et al. Multifractal Topography of Several Planetary Bodies in the Solar System. arXiv:1805.11249. When this website went online in the early 2000s, observations of a naturally pervasive self-similar geometry were spurious if at all. Here geophysicists Landais and Frederic Schmidt, Universite Paris-Saclay, and Shaun Lovejoy, McGill University evince a self-similar mathematical presence across our home stellar array. See also Universal Multifractal Martian Topography by this team in Nonlinear Processes in Geophysics (22/6, 2015).

Topography is the expression of both internal and external processes of a planetary body. We propose here to use the multifractal approach to describe fields of topography. This theory both encompass height and slopes and other statistical moment of the field, tacking into account the scale invariance. As we commonly observe the juxtapostion of rough and smooth at given scale, the multifractal framework seems to be appropriate for hypsometric studies. Here we analyze the data at global scale of the Earth, Mars, Mercury and the Moon and find that the statistics are in good agreement with the multifractal theory for scale larger than 10km. Surprisingly, the analysis shows that all bodies have the same fractal behavior for scale smaller than 10km. (Abstract excerpts)

Lapidus, Michel. An Overview of Complex Fractal Dimensions. arXiv:1803.10399. The French-American, UC Riverside polymathematician posts a latest intricate, 100+ page, contribution about nature’s intrinsic, structural self-similarities. Visit the author’s website for a lifetime lists of papers and books such as Fractal Geometry, Complex Dimensions and Zeta Functions (Springer 2013). Since our sapient emergence arises from these same geometric codes, when might we see ourselves as their way of reaching conscious recognition, so as we may carry forth to a new creation?

Laskin, Nick. Fractals and Quantum Mechanics. Chaos. 10/4, 2000. A novel hypothesis of a “fractional quantum physics” as an indication of its fundamentally discrete, self-similar character.

Liang, L., et al. Self-Similarities and Power-laws in the Time-resolved Spectra of GRB 190114C, 130427A, 160509A, and 160625B. arXiv:1910.12615. In an entry to appear in Astronomy & Astrophysics, five scientists at the International Center for Relativistic Astrophysics Network, Pescara, Italy report upon the title Gamma Ray Burst (GRB) phenomena as it exemplifies a natural fractal display.

Conclusion: The most far reaching discovery of self-similarities and power-laws are extensively confirmed, thanks also to the conclusions presented in the companion papers, which leads to the existence of a discrete quantized repetitive polarized emission on a timescale as short as 10−14s. These results open new paths in the discovery of fundamental physical laws.

Lima, J. A. S. and R. E. de Souza. Power-law Stellar Distributions. Physica A. 350/303, 2005. Another example of how and where nonlinear self-similarities are being found on interstellar scales.

Liu, Qin. Towards a Fractal Approach to Hadronization. Physica A. 338/1-2, 2004. One more example of the intensifying global discovery of a self-similar universality from quanta to humankind.

Financial markets and those at the subnuclear level of matter are very much the same. (42)

Maeder, Andre. Evolution of the Early Universe in the Scale Invariant Theory. arXiv:1902.10115. The Geneva Observatory astronomer (search) expands his collegial quantification of a universally repetitious self-similarity onto the whole evolutionary cosmos. See also The Growth of the Density Fluctuations in the Scale-Invariant Vacuum Theory by AM and Vesselin Gueorguiev at 1811.03495.

Analytical solutions are obtained for the early cosmological phases in the scale invariant models with curvature k=0. The physical properties in the radiative era are derived from conservation laws and compared to those of current standard models. The critical runs of the temperature and of the expansion rate of the scale invariant models with low densities, are quite similar at the time of nucleosynthesis to those of standard models, leading to the same freezing number ratio of neutrons to protons. These results are consistent with the fact that the scale invariant models appear to not require the presence of dark matter. (Abstract)

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