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Journal articles on the topic 'Fractal universe'

Author: Grafiati

Published: 2 June 2025

Last updated: 19 July 2025

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1

Pietronero, Luciano, and Francesco Sylos Labini. "Fractal universe." Physica A: Statistical Mechanics and its Applications 280, no. 1-2 (2000): 125–30. http://dx.doi.org/10.1016/s0378-4371(99)00627-5.

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2

Ziep, Otto. "Fractal Universe and Atoms." Scholars Journal of Physics, Mathematics and Statistics 12, no. 04 (2025): 89–96. https://doi.org/10.36347/sjpms.2025.v12i04.002.

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Fractal universes and atoms are assigned to k-components or stable orbiting laps of simplest cycles of elliptic invariants. Cosmological redshift, expansion of the universe, origin of cosmic rays, cosmic microwave background, quantum entanglement and the cosmological constant problem are resolvable easily by fractal universes of bifurcating spacetime. Quantum entanglement is explainable by a highly correlated pseudo-congruent k-component in bifurcating spacetime. A one-dimensional complex contour around nontrivial zeros of zeta and L- functions is capable to create a zero-energy universe- action functional. Gauge coupling parameter fit into Gaussian periods of fixpoints. Many experiments in natural history support a fractal zeta universe.

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3

FANG, L. Z., H. J. MO, and H. G. BI. "SELF-AFFINITY OF THE LARGE SCALE STRUCTURE OF THE UNIVERSE." Modern Physics Letters A 02, no. 07 (1987): 473–78. http://dx.doi.org/10.1142/s0217732387000586.

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The large scale structure of the universe is not self-similar, but may be self-affine. A cosmic string model with two self-affine fractals has been developed. All statistical features, such as 1) r−1.8 law; 2) dependence of correlation strength on objects; 3) flattened tail in correlation function; 4) bubble structure; 5) dependence of correlation length on the size of sample, can be explained if the local fractal is taken to be 1.2 and the global fractal to be 2.4.

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4

Sheykhi, Ahmad, Zeinab Teimoori, and Bin Wang. "Thermodynamics of fractal universe." Physics Letters B 718, no. 4-5 (2013): 1203–7. http://dx.doi.org/10.1016/j.physletb.2012.12.072.

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5

COLEMAN, PAUL H. "FRACTALS AND THE UNIVERSE." Fractals 03, no. 03 (1995): 567–79. http://dx.doi.org/10.1142/s0218348x95000503.

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Many examples of fractal geometry are seen in the field of Astronomy, from nearby objects such as our Sun, to phenomena at intermediate length scales in our Galaxy such as the distribution of masers. This paper will give many examples of various length scales and finally concentrates on the largest scales which can be probed in our universe, with analyses of locations of galaxies. It has been known for some twenty years that the distribution of galaxies on small scales is fractal. This is seen in analyses which indicate that both galaxies and their clusters are power law correlated (a signature of fractal behavior). At larger length scales the distribution is supposed to exhibit a so-called correlation length and was thought to then become homogeneous—except for occasional fluctuations. More data and subsequent analysis have shown that these fluctuations are anything but occasional, as structures are seen to exist on length scales up to the maximum scales which can be probed with the new data. By reanalyzing the data, with methods that are particularly suited to fractal distributions, one finds no correlation length at all—indicating that the fractal structure may extend up to perhaps the largest length scales possible. Analysis also indicates that when galaxy masses are considered, the distribution may be multifractal. These conclusions have serious implications for many subfields in astrophysics today, from galaxy formation to the Robertson-Walker metric of spacetime.

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Casarosa, Matteo. "A Fractal Universe and the Identity of Indescernibles." Stance: An International Undergraduate Philosophy Journal 12 (2019): 86–94. http://dx.doi.org/10.5840/stance2019128.

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The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those from classical symmetric universes three main objections put forth against this kind of arguments.

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Casarosa, Matteo. "A Fractal Universe and the Identity of Indiscernibles." Stance: an international undergraduate philosophy journal 12, no. 1 (2019): 86–95. http://dx.doi.org/10.33043/s.12.1.86-95.

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The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those from classical symmetric universes three main objections put forth against this kind of arguments.

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8

Pichalakkattu, Binoy. "Mysticism in the Fractal Structure of the Universe." Tattva Journal of Philosophy 4, no. 2 (2012): 121–38. http://dx.doi.org/10.12726/tjp.8.8.

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In this paper a critical enquiry is made into the mystical dimension of science with specific reference to contemporary developments in fractal Geometry. The paper begins with a historical synthesis of the mystical roots of science to see how science lost its mystical nature, especially in the modern era, corresponding to the emergence of a dualistics world-view in philosophy. However, contemporary science, very specially 'fractals', takes us to a mystical realm in which the dichotomised world-views of matter-spirit, finite-infinite, microcosm and macrocosm are blurred. Such a mystical understanding re-defines and transcends the traditional understanding of mysticism which is confined to the sacred spheres.

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9

Martínez, V. J. "COSMOLOGY:Enhanced: Is the Universe Fractal?" Science 284, no. 5413 (1999): 445–46. http://dx.doi.org/10.1126/science.284.5413.445.

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10

TERAZAWA, HIDEZUMI. "FRACTAL SUBSTRUCTURES OF THE UNIVERSE." Modern Physics Letters A 13, no. 35 (1998): 2801–6. http://dx.doi.org/10.1142/s0217732398002977.

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It is pointed out that the universe has fractal substructures such as clusters of galaxies, galaxies, clusters of stellar systems, and stellar systems due to the scaling properties in these gravitational subsystem with respect to the numbers and masses of constituents, and the size-scales and time-scales of substructures. Also suggested is a clue to explain both the "less-large-number hypothetical relations" of NG~NS(~NC~1011) where NG and NS(NC) are the "total number of galaxies" in the universe and the average total number of stars in a galaxy (the average total number of comets in a solar system), respectively, and the "even-less-large-number hypothetical relations" of n1~n2~n3(~103) for n1≡RU/DG, n2≡DG/RG and n3≡RG/DS where RU(RG) is the "radius of the universe" (the average radius of an ordinary galaxy) and DG(DS) is the average distance between two neighboring galaxies (that between two neighboring stars).

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11

de Gouveia Dal Pino, E. M., A. Hetem, J. E. Horvath, and T. Villela. "Is the Early Universe Fractal?" Symposium - International Astronomical Union 168 (1996): 465–66. http://dx.doi.org/10.1017/s007418090011037x.

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It is generally believed that onverylarge scales the distribution of matter in the universe is homogeneous and effectively all the existing theoretical approaches are based on this assumption. However, recent re-analysis of galaxy-galaxy and cluster-cluster correlations by Coleman and Pietronero (1992, hereafter CP) and Luo and Schramm (1992, hereafter LS) indicates that the distribution of the visible matter in the universe is fractal or multifractal up to the present observed limits (~100 h−1Mpc for H0= 100 h km s−1Mpc−1and 0.5≤h≤1) without any evidence for homogenization on those scales. The fractal dimension obtained from these analyses is D ~ 1.2 - 1.3 (CP; LS).

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12

Grinchenko, Victor, and Volodymyr Matsypura. "FRACTALIST." In the world of mathematics, no. 1 (2) (2024): 60–87. https://doi.org/10.17721/1029-4171.2024/2.9.

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The article is dedicated to the 100-th anniversary of the birth of Benoit Mandelbrot, the man who coined the word ''fractal'' and, in fact, became the author of a new direction in science - fractal geometry. The article briefly presents his biography, discusses the definition of the concept of fractal. Some attention is paid to Mandelbrot's predecessors and it is considered that it was B. Mandelbrot, thanks to his erudition and encyclopedic knowledge, who was able to systematize a huge number of previously known and newly discovered fractals. Today, fractals constitute an important section of modern science. This is Mandelbrot's main merit. His works continue to inspire researchers and artists, proving that mathematics is not only a tool for understanding the Universe, but also a source of beauty and creativity.

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Macdonald, Blair. "Experiment on Inverted Fractal Corresponds with Cosmological Observations and Conjectures." International Journal of Quantum Foundations 6, no. 1 (2023): 1–32. https://doi.org/10.5281/zenodo.10493227.

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In a recent paper—The Fractal Corresponds to Light and Quantum Foundation Problems—the author described the forward-looking progressive perspective of a fractal. In this paper the author modelled the complementary and dual perspective of the same fractal: its retrospective perspective, this time it pertaining specifically to cosmology. Recent discussions as to whether the universe is fractal concluded with the 2012 WiggleZ Dark Energy Survey findings in (part) agreement with fractal-cosmology proponents that the small-scale observable universe is fractal; however, beyond this, the smooth large-scale—and thus the universe—is not fractal. Is this smoothness and other ΛCDM properties what one would expect to observe (within) if the universe is a fractal? Current fractal-cosmology models seek repeating patterns of larger scale further out. Though these structures have since been found in the smooth; in this paper the growth from the perspective within a growing fractal was modelled. An experiment was conducted on a ‘simple’ (Koch snowflake) fractal. New triangle sizes of arbitrary size were held constant and earlier triangles were allowed to expand as the fractal set iterated (grew). Classical kinematic equations—velocity and acceleration—were calculated for the total area total and the distance between arbitrary points. Hubble-Lemaitre’s Law, accelerated expansion, and changing size distribution, all corresponding to cosmological observations and conjectures were tested for. Results showed: the area expanded exponentially from an arbitrary starting size; and as a consequence, the distances between measured points—from any location within the set—receded away from the ‘observer’ at increasing velocities and accelerations. It was concluded, the universe is not only fractal, but that it is a fractal. At the expense of the cosmological principle, the fractal is a geometrical match to the cosmological observations and conjectures, able to demonstrate the inflation epoch, Hubble-Lemaitre and accelerated expansion. The large-scale smoothness is a property of a growing fractal and is expected. From this model— from planet Earth— we are observing within ‘the branches’ looking out and back in time to ‘the boughs’ (the large quasar structures) and ‘the trunk’ (the CMB—which was once seedling sized Planck area size) of a fractal shaped universe. Other problems—including the horizon problem and the vacuum catastrophe—were addressed. Based on a previous work on the quantum with the fractal, the fractal may offer a direct mechanism to marrying quantum problems with cosmological problems—unifying the two realities as being two aspects of the same modern geometry.

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14

Gaite, Jose. "Scale Symmetry in the Universe." Symmetry 12, no. 4 (2020): 597. http://dx.doi.org/10.3390/sym12040597.

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Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale invariant distribution of matter, namely it gives rise to a fractal geometry. A suitable explanation of the features of the fractal cosmic mass distribution is provided by the nonlinear Poisson–Boltzmann–Emden equation. An alternative interpretation of this equation is connected with theories of quantum gravity. We study the fractal solutions of the equation and connect them with the statistical theory of random multiplicative cascades, which originated in the theory of fluid turbulence. The type of multifractal mass distributions so obtained agrees with results from the analysis of cosmological simulations and of observations of the galaxy distribution.

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15

YOSHINO, D., and H. SAGAWA. "MONTE CARLO SIMULATION OF SPIRAL GALAXY FORMATION." Fractals 16, no. 02 (2008): 119–27. http://dx.doi.org/10.1142/s0218348x08003922.

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We perform the Monte Carlo simulation of the spiral galaxy formation by using a model which includes the effect of shockwave of supernova explosion in the stochastic process for the star formation. We analyze the fractal dimension of the spiral galaxy obtained by the two-point correlation function method. The calculated fractal dimensions are discussed in comparison with those of the present universe and the early universe. In our simulation, the fractal dimension is obtained as D ≈ 1.3, which is close to the value of the present universe.

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16

Maddox, John. "The Universe as a fractal structure." Nature 329, no. 6136 (1987): 195. http://dx.doi.org/10.1038/329195a0.

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17

Coleman, Paul H., and Luciano Pietronero. "The fractal structure of the universe." Physics Reports 213, no. 6 (1992): 311–89. http://dx.doi.org/10.1016/0370-1573(92)90112-d.

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18

Iovane, G., E. Laserra, and F. S. Tortoriello. "Stochastic self-similar and fractal universe." Chaos, Solitons & Fractals 20, no. 3 (2004): 415–26. http://dx.doi.org/10.1016/j.chaos.2003.08.004.

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19

Joyce, M., P. W. Anderson, M. Montuori, L. Pietronero, and F. Sylos Labini. "Fractal cosmology in an open universe." Europhysics Letters (EPL) 50, no. 3 (2000): 416–22. http://dx.doi.org/10.1209/epl/i2000-00285-3.

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20

Coleman, Paul H., and Luciano Pietronero. "The fractal nature of the universe." Physica A: Statistical Mechanics and its Applications 185, no. 1-4 (1992): 45–55. http://dx.doi.org/10.1016/0378-4371(92)90436-t.

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21

Ziep, Otto. "A Quantum Entangled Fractal Superfluid Universe." Journal of High Energy Physics, Gravitation and Cosmology 11, no. 03 (2025): 850–68. https://doi.org/10.4236/jhepgc.2025.113054.

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22

Maia Shevardenidze, Maia Shevardenidze. "Fractals and Forecasting of Economic Cycles." Economics 105, no. 09-10 (2022): 32–39. http://dx.doi.org/10.36962/ecs105/9-10/2022-32.

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For many centuries, scientists have used classical methods of calculation in the process of exploring and modeling the universe. And such functions that did not carry the proper smoothness or regularity were often considered as pathologies and were not given much attention. The fractal geometry of Benoit Mandelbrot deals with the study of such irregular sets. The basic concept of fractal geometry is a fractal, the origin of which is associated with computer modeling. With the help of fractals, it was possible to describe the glow of the sky during a thunderstorm, the dynamics of the growth of tree branches, the fractal structure of the internal organs of a person, the psyche and organizational systems, etc. Recently, fractals have been widely used to study economic cycles. In particular, such a characteristic of a time series as fractal dimension makes it possible to determine the moment when the system becomes unstable and is ready to move to a new state. Modern science widely uses the theory of fractals to study time series in order to increase the reliability of forecasting economic dynamics. The main feature of a fractal is the infinite repetition of a self-similar structure in different scales. Analogous nature characterizes economic cycles. Samuelson and Hicks created an appropriate mathematical model for modeling economic cycles, later this approach was developed in the works of Goodwin. Recently, fractals have been widely used to study economic processes. To date, there are many different mathematical models of fractals, each of which differs from the others in a certain recursive function. With the help of methods of fractal analysis and their modifications, it is possible to determine moments of qualitative change in the behavior of the system and, accordingly, to predict their subsequent behavior in a relatively long-term perspective. The most urgent task, solved by the methods developed within this approach, is the identification of the moment of the onset of major economic crises, that is, forecasting them in the near future. Keywords: Fractals. Economic cycles. Prognosis.

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23

Karami, K., Mubasher Jamil, S. Ghaffari, K. Fahimi, and R. Myrzakulov. "Holographic, new agegraphic, and ghost dark energy models in fractal cosmology." Canadian Journal of Physics 91, no. 10 (2013): 770–76. http://dx.doi.org/10.1139/cjp-2013-0293.

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We investigate the holographic, new agegraphic, and ghost dark energy models in the framework of fractal cosmology. We consider a fractal flat Friedmann–Robertson–Walker universe filled with dark energy and matter. We obtain the deceleration and equation of state parameters of the selected dark energy models in the ultraviolet regime and discuss their implications in the early universe.

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SLOBODRIAN, R. "Fractal cosmogony: similarity of the early universe to microscopic fractal aggregates." Chaos, Solitons & Fractals 23, no. 3 (2005): 727–29. http://dx.doi.org/10.1016/s0960-0779(04)00341-8.

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25

Vavilova, I. B. "On the Use of Fractal Concepts in Analysis of Distributions of Galaxies." Symposium - International Astronomical Union 168 (1996): 473–75. http://dx.doi.org/10.1017/s007418090011040x.

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The well- grounded polemics about the fractal structure of the Universe and a new cosmological picture which appears in connection with this, in first instance the absence of any evidence for homogenization up to present observational limits 200h−1Mpc, have been detailed at the work by Coleman, Pietronero (1992). Two versions on nature of fractal pattern of the galaxy distribution in the observed universe also are now: it behaves like a simple homogeneous fractal (Pietronero 1987; Coleman et al. 1988) and as a multifractal - fractal having more than one scaling index (Jones et al. 1988; Martinez, Jones 1990; Martinez et al. 1990; Borgani et al. 1993 (with the good review for matter of above)).This work does not play decisively into hands of these versions so the fractal concepts, exactly a selfsimilarity and multifractal, were applied here for the analysis oftwo - dimensionaldistribution of thebrightgalaxies and dwarf galaxies of the low surface brightness (LSBD) belonging to the Local Supercluster (LS). But if the observed universe holds the fractal structure, so it is useful to trace over the lower fractal pattern on the small scales of clustering of galaxies within the framework of the known superclusters and, in the first instance, within the local overdensity of galaxies. This work is a preliminary before preparing one with the same analysis of three- dimensional distribution of galaxies of LS.

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26

Tao, Yong. "Quantum Behavior Arises Because Our Universe is a Fractal." Reports in Advances of Physical Sciences 01, no. 02 (2017): 1750006. http://dx.doi.org/10.1142/s2424942417500062.

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To explain the origin of quantum behavior, we propose a fractal calculus to describe the non-local property of the fractal curve [Y. Tao, J. Appl. Math. 2013 (2013) 308691]. This study demonstrates that if the dimension of time axis is slightly less than 1, then Planck’s energy quantum formula will naturally emerge. In this paper, we further show that if the dimension of time axis is less than 1, Heisenberg’s Principle of Uncertainty will emerge as well. Our finding implies that fractal calculus may be an intrinsic way of describing quantum behavior. To test our theory, we also provide an experimental proposal for measuring the dimension of time axis.

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Shahzad, Muhammad Umair, Ayesha Iqbal, and Abdul Jawad. "Dynamical Properties of Dark Energy Models in Fractal Universe." Symmetry 11, no. 9 (2019): 1174. http://dx.doi.org/10.3390/sym11091174.

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In this paper, we consider the flat FRW spacetime filled with interacting dark energy and dark matter in fractal universe. We work with the three models of dark energy named as Tsallis, Renyi and Sharma–Mittal. We investigate different cosmological implications such as equation of state parameter, squared speed of sound, deceleration parameter, statefinder parameters, ω e f f - ω e f f ´ (where prime indicates the derivative with respect to ln a , and a is cosmic scale factor) plane and Om diagnostic. We explore these parameters graphically to study the evolving universe. We compare the consistency of dark energy models with the accelerating universe observational data. All three models are stable in fractal universe and support accelerated expansion of the universe.

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Puetz, Stephen J. "The infinitely fractal universe paradigm and consupponibility." Chaos, Solitons & Fractals 158 (May 2022): 112065. http://dx.doi.org/10.1016/j.chaos.2022.112065.

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29

Martínez, Vicent J., and Bernard J. T. Jones. "Why the Universe is not a fractal." Monthly Notices of the Royal Astronomical Society 242, no. 4 (1990): 517–21. http://dx.doi.org/10.1093/mnras/242.4.517.

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Jawad, Abdul, Shamaila Rani, Ines G. Salako, and Faiza Gulshan. "Pilgrim dark energy models in fractal universe." International Journal of Modern Physics D 26, no. 06 (2016): 1750049. http://dx.doi.org/10.1142/s0218271817500493.

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We discuss the cosmological implications of interacting pilgrim dark energy (PDE) models (with Hubble, Granda–Oliveros and generalized ghost cutoffs) with cold dark matter ([Formula: see text]CDM) in fractal cosmology by assuming the flat universe. We observe that the Hubble parameter lies within observational suggested ranges while deceleration parameter represents the accelerated expansion behavior of the universe. The equation of state (EoS) parameter ([Formula: see text]) corresponds to the quintessence region and phantom region for different cases of [Formula: see text]. Further, we can see that [Formula: see text]–[Formula: see text] (where prime indicates the derivative with respect to natural logarithmic of scale factor) plane describes the freezing and thawing regions and also corresponds to [Formula: see text] limit for some cases of [Formula: see text] (PDE parameter). It is also noted that the [Formula: see text]–[Formula: see text] (state-finder parameters) plane corresponds to [Formula: see text] limit and also shows the Chaplygin as well as phantom/quintessence behavior. It is observed that pilgrim dark energy models in fractal cosmology expressed the consistent behavior with recent observational schemes.

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Roscoe, D. F. "Discrete spatial scales in a fractal universe." Astrophysics and Space Science 244, no. 1-2 (1996): 231–48. http://dx.doi.org/10.1007/bf00642295.

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Ghaffari, S., E. Sadri, and A. H. Ziaie. "Tsallis holographic dark energy in fractal universe." Modern Physics Letters A 35, no. 14 (2020): 2050107. http://dx.doi.org/10.1142/s0217732320501072.

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We study the cosmological consequences of interacting Tsallis holographic dark energy model in the framework of the fractal universe in which the Hubble radius is considered as the IR cutoff. We derive the equation of state (EoS) parameter, deceleration parameter and the evolution equation for the Tsallis holographic dark energy density parameter. Our study shows that this model can describe the current accelerating universe in both non-interacting and interacting scenarios, and also a transition occurs from the deceleration phase to the accelerated phase at the late-time. Finally, we check the compatibility of free parameters of the model with the latest observational results by using the Pantheon supernovae data, eBOSS, 6df, BOSS DR12, CMB Planck 2015, Gamma-Ray Burst.

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33

Trivedi, Kirti. "Hindu temples: Models of a fractal universe." Visual Computer 5, no. 4 (1989): 243–58. http://dx.doi.org/10.1007/bf02153753.

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Aryal, Mukunda, and Alexander Vilenkin. "The fractal dimension of the inflationary universe." Physics Letters B 199, no. 3 (1987): 351–57. http://dx.doi.org/10.1016/0370-2693(87)90932-4.

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Retnaningsih, Retnaningsih. "Fractal Geometry, Fibonacci Numbers, Golden Ratios, And Pascal Triangles as Designs." Journal of Academic Science 1, no. 1 (2024): 51–66. http://dx.doi.org/10.59613/msd4n328.

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Fractal geometry is a part of mathematics that discusses the shape of fractals or any form that is self-similarity. A fractal can be broken down into parts that are all similar to the original fractal. Fractals have infinite detail and can have self-similar structures at different magnifications. In many cases, a fractal can be generated by repeating a pattern, which is usually in a recursive or iterative process. In mathematics and art, two values are considered to be a golden ratio relationship if the ratio between the sum of the two values to the large value is equal to the ratio between the large value to the small value. A Fibonacci sequence is a sequence of numbers that has a unique shape. The first term of this sequence of numbers is 1, then the second term is also 1, then for the third term it is determined by adding the two previous terms so that a sequence of numbers with a certain pattern is obtained. Pascal's triangle is a geometric rule of binomial coefficients in a triangle. Shapes that resemble fractal geometry, golden ratios and Fibonacci numbers are found in many places in this realm, for example the shapes of various plants, animals, as well as in humans themselves, even the universe. This fractal geometry can also be used to design batik motif creations, architectural design or musical art. This paper describes how a fractal object can be made with geometric transformations that can be used to develop batik motif creations. And also look at the relationship between fractal geometry, the golden ratio, Fibonacci numbers, and Pascal's triangles and the shapes of these shapes that exist in this nature.

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Rani, Mamta, and Sanjeev Kumar Prasad. "Superior Cantor Sets and Superior Devil Staircases." International Journal of Artificial Life Research 1, no. 1 (2010): 78–84. http://dx.doi.org/10.4018/jalr.2010102106.

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Mandelbrot, in 1975, coined the term fractal and included Cantor set as a classical example of fractals. The Cantor set has wide applications in real world problems from strange attractors of nonlinear dynamical systems to the distribution of galaxies in the universe (Schroder, 1990). In this article, we obtain superior Cantor sets and present them graphically by superior devil’s staircases. Further, based on their method of generation, we put them into two categories.

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FANG, L. Z. "FRACTAL OF LARGE SCALE STRUCTURE IN THE UNIVERSE." Modern Physics Letters A 01, no. 11 (1986): 601–5. http://dx.doi.org/10.1142/s0217732386000762.

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McCauley, Joseph L. "The Galaxy Distribution." Fractals 06, no. 02 (1998): 109–19. http://dx.doi.org/10.1142/s0218348x98000134.

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From the standpoint of theoretical physics we can treat Newtonian cosmology as a problem in nonlinear dynamics. The attempt to average the density, in search of a method of making contact between theory and observation, is replaced by the more systematic idea of coarsegraining. I also explain in this context why two previous attempts at the construction of hierarchical models of the universe are not useful for data analysis. The main ideas behind two older competing data analyses purporting to show evidence from galaxy statistics for either a homogeneous and isotropic universe in one case, and for a mono-fractal universe in the other, are presented and discussed. I also present the method and results of a newer data analysis that shows that visible matter provides no evidence that would allow us to claim that the cosmological principle holds, or that the universe is fractal (or multifractal). In other words, observational data provides us with no evidence that the universe is either homogeneous and isotropic, or monofractal.

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TREGUBOVA, I. A. "FRACTAL GRAPHICS FOR VIRTUAL ENVIRONMENT GENERATION." Digital Technologies 26 (2019): 29–35. http://dx.doi.org/10.33243/2313-7010-26-29-35.

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Progress in hardware and software development is impressively fast. The main reason of computer graphics fast improvement is a full experience that can be reached though visual representation of our world. Therefore, the most interesting problem of it is a realistic image with high quality and resolution, which often requires procedural graphics generation. The article analyzes simplicity of a fractal and mathematics abstraction. Mathematics describes not only accuracy and logic but also beauty of the Universe. Mountains, clouds, trees, cells do not fit into the world of Euclidean geometry. They cannot be described by its methods. But fractals and fractal geometry solve that problem. Fractals are fairly simple equations on a sheet of paper with bright, unusual images, and, above all, they explain things. Fractal is a figure in the space, which consists of statistical character as the whole. It is self-similar, and therefore looks ‘roughly’ same and does not depend on its scale. So, any complex object can be called a fractal, if it has the same shape, as the parts it consists of. Fractal is abstract, and it helps to translate any algebraic problem into geometric, where solution is always obvious. A lot of researches in the field of fractal graphics has been carried out, but there are still issues that deserve considerable attention and more perfect solutions. The main purpose of the work is codes development with object-oriented programming languages for fractal graphics rendering. The article analyzes simplicity of a fractal and mathematics abstraction. Procedural generation was described as a method of algorithmic data generation for 3D models and textures creation. Code was written with general-purpose programming language Python, which renders step by step creation of fractal composition and variations of fractal images. Fractal generation used for modeling is part of realism in computer graphics In summary, procedural generation is very important for video games, as it can be used to automatically create large amount of game content. The random generation of natural looking landscapes is based on geometric computer generated images Created compositions can be used in computer science for image compression, in medicine for the study of the cellular level of organs, etc.

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Einasto, Jaan. "Formation of the Structure of the Universe: Observational Aspects." Australian Journal of Physics 43, no. 2 (1990): 145. http://dx.doi.org/10.1071/ph900145.

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A review of recent developments in the study of the structure of the universe is given. We focus on two problems: the fractal description of the universe, and on observational constraints on the bias in galaxy formation.

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Bojowald, Martin, and Ari Gluckman. "Chaos in a tunneling universe." Journal of Cosmology and Astroparticle Physics 2023, no. 11 (2023): 052. http://dx.doi.org/10.1088/1475-7516/2023/11/052.

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Abstract A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum dynamics, captured by new quasiclassical methods. Chaotic dynamics in the early universe, described by such models, implies that a larger set of initial values of an expanding branch can be probed.

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Banerjee, S. N., B. Chakrabarti, and A. Bhattacharya. "On the Structure of the Early Universe." Modern Physics Letters A 12, no. 08 (1997): 573–79. http://dx.doi.org/10.1142/s0217732397000595.

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We have postulated that the mass of the early universe possesses a (mass) fractal dimension 'd' during the early stages of its expansion and so we have come across many interesting consequences of the early universe lying in between matter and radiation dominated limits of it.

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Carrasco Inglés, José Luis. "Deciphering the Universe as a Quantum Information Network." International Journal of Science and Engineering Invention 10, no. 06 (2024): 38–44. https://doi.org/10.23958/ijsei/vol10-i09/269.

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This article proposes a new approach to understanding the structure of the Universe through the identification of three-dimensional fractal patterns based on the golden ratio that emerge from the mathematical sequences of Fibonacci, Lucas and a new sequence called Carrasco. The research through the analysis of the digital roots of these sequences and their geometric representation suggests that the Universe can operate as a self-organised quantum information network, where each point of the network has information from the rest of the points and interacts by exchanging it bidirectionally, contributing to its evolution due to the arrangement of the information in space-time that is structured in golden ratio. The fractal patterns discovered are organized in cyclic hexagonal structures following the golden ratio. This finding makes it possible to describe the Universe as a self-organising holographic system, capable of storing and transmitting information efficiently across different scales, from the quantum to the cosmological level. This approach unifies concepts from quantum physics, fractal geometry and cosmology, offering an alternative perspective to conventional cosmological theories. These results could have significant implications for fundamental physics, biology and quantum technologies, providing a basis for the creation of new tools and applications in quantum computing, artificial intelligence and advanced materials. This study expands our understanding of the relationship between geometry, information and the structure of the Universe.

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Grujic, P. V. "The concept of fractal cosmos: III. Present state." Serbian Astronomical Journal, no. 182 (2011): 1–16. http://dx.doi.org/10.2298/saj1182001g.

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This is the sequel to the previous accounts on the rise and development of the concept of fractal cosmos, up to year 2001 (Grujic 2001, 2002). Here we give an overview of the present-day state of art, with the emphasis on the latest developments and controversies concerning the model of hierarchical universe. We describe both the theoretical advances and the latest empirical evidence concerning the observation of the large-scale structure of the observable universe. Finally we address a number of epistemological points, putting the fractal paradigm into a broader cosmological frame.

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Bose, Akash, and Subenoy Chakraborty. "Does fractal universe favour warm inflation: Observational support?" Nuclear Physics B 978 (May 2022): 115767. http://dx.doi.org/10.1016/j.nuclphysb.2022.115767.

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Harrison, Ruth M. "Poe Möbius: An Exploration of Poe's Fractal Universe." Poe Studies/Dark Romanticism 36, no. 1-2 (2003): 32–44. http://dx.doi.org/10.1111/j.1754-6095.2003.tb00148.x.

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Botke, J. C. "Thoughts Concerning the Origin of Our Fractal Universe." Journal of Modern Physics 16, no. 01 (2025): 167–97. https://doi.org/10.4236/jmp.2025.161008.

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Chen, Sheena, and Tong-Jie Zhang. "Search for Extraterrestrial Intelligence (SETI) by fractal universe." Results in Physics 15 (December 2019): 102548. http://dx.doi.org/10.1016/j.rinp.2019.102548.

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Slezak, Michael. "Fractal universe theories shaken up by WiggleZ survey." New Scientist 215, no. 2880 (2012): 11. http://dx.doi.org/10.1016/s0262-4079(12)62243-x.

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Rozgacheva, Irina. "Do Fractals Confirm the General Theory of Relativity?" Symmetry 11, no. 6 (2019): 740. http://dx.doi.org/10.3390/sym11060740.

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The relatively high abundance of fractal properties of complex systems on Earth and in space is considered an argument in support of the general relativity of the geometric theory of gravity. The fractality may be called the fractal symmetry of physical interactions providing self-similarities of complex systems. Fractal symmetry is discrete. A class of geometric solutions of the general relativity equations for a complex scalar field is offered. This class allows analogy to spatial fractals in large-scale structures of the universe due to its invariance with respect to the discrete scale transformation of the interval d s ↔ q d s ˜ . The method of constructing such solutions is described. As an application, the treatment of spatial variations of the Hubble constant H 0 H S T (Riess et al., 2016) is considered. It is noted that the values H 0 H S T form an almost fractal set. It has been shown that: a) the variation H 0 H S T may be connected with the local gravitational perturbations of the space-time metrics in the vicinity of the galaxies containing Cepheids and supernovae selected for measurements; b) the value of the variation H 0 H S T can be a consequence of variations in the space-time metric on the outskirts of the local supercluster, and their self-similarity indicates the fractal distribution of matter in this region.

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