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III. An Organic, Conducive, Habitable MultiUniVerse

F. Systems Cosmology: Fractal SpaceTimeMatter

De la Fuente Marcos, R. and C. Multifractal Evolution in Interacting Galaxies. Monthly Notices of the Royal Astronomical Society. 372/279, 2006. Suffolk University, Madrid campus, astronomers quantify the self-similar geometries that result via celestial confluences from supergiant clouds to stellar superclusters.

Multifractality can be understood as superposition of different fractal patterns. (280)

De Vega, H., et al. Fractal Structures and Scaling Laws in the Universe. Chaos, Solitons & Fractals. 10/2-3, 1999. More mathematical insights into nature’s iterative geometry.

Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10-4pc till 100pc. Secondly, the galaxy distribution has been observed to be fractal in scales up to hundreds of Mpc.” (329) (pc = parsecs = 3.26 light years).

Demianski, Marek and Andrei Doroshkevich. Self Similarity of the Dark Matter Dominated Objects and the Shape of Small Scale Power Spectrum. arXiv:1701.03474. A latest posting by University of Warsaw and Lebedev Physical Institute of the Russian Academy of Sciences, senior astrophysicists contributes to global understandings of an iterative cosmic topology and emergence which seems trying to achieve self-recognition through its worldwise human phenomenon.

One of the important goals of cosmology is to establish correlations between the observed Universe – the CMB, Large Scale Structure (LSS), galaxies etc. – and the processes that occurred at the earlier epochs of evolution of the Universe and are encoded in the initial power spectrum of density perturbations. For larger scale D > 10Mpc this problem is approximately solved by the CMB observations of the WMAP missions and is realized as the standard ΛCDM model. However the shape of the power spectrum at small scale remains unknown and its investigation is one of the actual current problem of cosmology. Now it is unfortunately not possible to obtain reliable information about this very important issue. Next very interesting problem is the universality and the self similarity of the internal structure of DM dominated halos in a wide range of their masses and sizes. (1)

Deppman, Airton. Fractal Structure of Hadrons: Experimental and Theoretical Signatures. Universe. Online August, 2017. It is ever amazing that we peoples can proceed altogether to plumb such physical depths and sidereal reaches. Here a University of Sao Paulo astrophysicist advises about an apparent intrinsic propensity of subatomic particles to form self-similar geometries. One then wonders as to where these mathematical lineaments came from, what other reality or persona might have put them there for a purpose?

One important ingredient in the study of cosmological evolution is the equation of state of the primordial matter formed in the first stages of the Universe. It is believed that the first matter produced was of hadronic nature, probably the quark–gluon plasma which has been studied in high-energy collisions. There are several experimental indications of self-similarity in hadronic systems—in particular in multiparticle production at high energies. Theoretically, this property was associated with the dynamics of particle production, but it is also possible to relate self-similarity to the hadron structure—in particular to a fractal structure of this system. In the present work, a review of the theoretical developments related to the thermodynamical properties of hadronic matter and its applications in other fields is presented. (Abstract)

Doering, Andreas and Tim Palmer. New Geometric Concepts in the Foundations of Physics. Philosophical Transactions of the Royal Society A. 373/Issue 2047, 2015. The Universitat Erlangen-Nurnberg and Oxford University physicists edit papers from a November 2013 workshop with this title that while admitting LHC Higgs boson and other successes, many problems remain out of reach for current theories. Led by Palmer (search) it is proposed that a more structural, topological approach might help resolve disparate issues. While the meeting included leaders such as Roger Penrose and Gerard ‘t Hooft, the 14 male authors each seemed to have one piece of the puzzle, with few attempts at an integral unity or vision. For example, Xavier Calumet considered a potential energy dependence of Planck’s constant; Cruz Morales and Zilber reformulated quantum mechanics using model theory; Andreas Doering reviewed the topos version of quantum theory; Chris Fewster presents locally covariant quantum field theories; Lucien Hardy proposes quantum theory in terms of bold tensors; Andrew Hodges does twistor geometry; Michael Lapidus presents fractal strings and the Riemann zeta function; Roger Penrose discusses the ‘googly problem’ within twistor cohomology; and Gerard ‘t Hooft (search) presents his programme for a classical, deterministic, real universe underlying quantum systems.

El Naschie, Mohamed. Fractal Black Holes and Information. Chaos, Solitons and Fractals. 29/1, 2006. The latest theories of the University of Alexandria, Egypt physicist that nature is deeply fractally self-similar in kind from quantum to celestial realms. El Naschie edits this highly technical monthly journal where many of his papers can be found. We are aware that he has been taken to task (2008) over this excess, and plans to resign, but feel this real natural recurrence merits expression.

Elbert, Oliver, et al. Core Formation in Dwarf Haloes with Self-Interacting Dark Matter. Monthly Notices of the Royal Astronomical Society. 453/1, 2015. A team of astrophysicists from UC Irvine, SciTech Analytics, and Ohio State University, including James Bullock conceiver of the theory, explore implications of a novel view of this ambient materiality which serves to fill out the large-scale cosmic structure. Since a static dark matter did not pass tests, Bullock wondered if it might interact with itself in a similar way as ponderable elements and chemicals, which has since gained credence. These inklings of an actively self-constructing universe compose an August 2015 Quanta Magazine article The Case for Complex Dark Matter.

Ferreira, Pedro, et al. Inflation in a Scale Invariant Universe. arXiv:1802.06069. When this section went online in 2004, only inklings of an inherent similarity across the range of celestial phenomena existed. Into the later 2010s, Oxford University, Fermi NAL, and ETH Zurich theorists, as they delve within global collaborations, can now post a theoretical affirmation. This consistent commonality is braced by a dense mathematics as it reveals a natural cosmos suffused, as tradition long intimated, with an infinite repetition in kind across the parsecs and billennia.


A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields - the spectral indices, the tensor to scalar ratio, the level of isocurvature modes and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale-symmetry broken phase, this theory is well described by a single scalar field theory. We find the predictions of this theory strongly compatible with current observations. (Abstract)

Fiete, Gregory and Alex de Lozanne. Seeing Quantum Fractals. Science. 327/652, 2010. University of Texas physicists use scanning, tunneling microscopy to discern indications of fractal forms in electronic structures of a magnetic Gallium Arsenide semiconductor, along with novel signs of a self-organized quantum criticality. (see also arXiv:0910.1338)

Fractals actually abound in nature: Galaxies, clouds, mountains, trees, and broccoli are all familiar examples. But fractals can occur in the quantum realm as well, even though they have never been observed, until, perhaps, now. (652)

Figueroa, Daniel, et al. Exact Scale-Invariant Background of Gravitational Waves from Cosmic Defects. Physics Review Letters. 110/101302, 2013. University of Geneva, University of Helsinki, and University of the Basque Country astrophysicists contribute instrumental and mathematical findings of self-ordering celestial processes across the parsecs as they array into nested stratifications which repeat the same phenomena everywhere. With such a scenario, one wonders what kind of universe is able to achieve, billions of years on, on a minute bioplanet, a modicum of its own self-witness, decipherment and description. For whatever purpose might we at some point ask about and awaken to?

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. (Abstract)

Fratini, Michela, et al. Scale-free Structural Organization of Oxygen Interstitials in La2CuO4+y.. Nature. 466/481, 2010. Italian and French physicists are able to detect pervasive nonlinear network geometries within this candidate superconducting material. Their innate, spontaneous presence might then be taken to suggest an independent, universal mathematical source.

It is also known that complex systems often have a scale-invariant structural organization, but hitherto none had been found in high-Tc materials. Here we report that the ordering of oxygen interstitials in the La2O2+y spacer layers of La2CuO4+y high-Tc superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 μm. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature. (481)

The data also raise the more intriguing question of whether the oxygen defects order on fractal networks because the electrons that form the strange metal constitute a ‘fractal glue,’ perhaps generated as a photographic-like image of the quantum critical charge fluctuations sampled during annealing (at temperatures well within the non-Fermi-liquid regime). (483)

Fujiwara, Noboru. The Scaling Rule for Environmental Organizing Systems in a Gravitational Field. BioSystems. 73/2, 2004. A computer scientist at the Nara Women’s University in Japan finds a constant, proportional relationship from unicellular organisms to humans and on to stellar dimensions. As cosmic and planetary evolution proceeds, it can be qualified by an increase in organized information. Fujiwara’s studies have been periodically published in this journal.

The present paper examines a scaling rule for the relationship between the integrated scaled metabolic energy and the mass of a system for a wide range of masses, from animals to 4He cores of main-sequence stars, considering the effect of gravitational energy. (111)

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