https://insu.hal.science/insu-00339735Miller, Bruce N.Bruce N.MillerDepartment of Physics and Astronomy [Fort Worth] - TCU - Texas Christian UniversityRouet, Jean-LouisJean-LouisRouetISTO - Institut des Sciences de la Terre d'Orléans - INSU - CNRS - Institut national des sciences de l'Univers - UO - Université d'Orléans - CNRS - Centre National de la Recherche ScientifiqueLe Guirriec, EmmanuelEmmanuelLe GuirriecMAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans - UO - Université d'Orléans - CNRS - Centre National de la Recherche ScientifiqueFractal geometry in an expanding, one-dimensional, Newtonian universeHAL CCSD2007[SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph][PHYS.PHYS.PHYS-GEO-PH] Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph][SDE.MCG] Environmental Sciences/Global ChangesPOTHIER, Nathalie2013-05-21 13:56:152023-05-01 03:24:082013-05-22 10:08:47enJournal articleshttps://insu.hal.science/insu-00339735/document10.1103/PhysRevE.76.036705application/pdf1Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the µ (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.