Abstract
This paper takes as established that the large scale distribution of galaxies includes a self-similar fractal range. The astonishing power of simple fractal algorithms to generate rich form is recalled and illustrated, then two issues are tackled. A) Does the fractal range stop at 5 Mpc, as asserted by Peebles et al.? Or does it continue beyond? Does it stop before the limits of observation? That is, should one believe the conventional statistical arguments in favor of 5 Mpc? B) The simplest fractal distributions are “fractally homogenous,” that is, homogeneous over a fractal set, and zero outside of this set. However, the distribution of galactic and inter-galactic mass is non homogenous to the extreme. It can be self-similar, in which case it follows a “multifractal measure,” as discussed by the author in 1974. This paper is concerned with questions of method, and analysis of data is not included.
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Mandelbrot, B.B. (1989). The Fractal Range of the Distribution of Galaxies; Crossover to Homogeneity, and Multifractals. In: Mezzetti, M., Giuricin, G., Mardirossian, F., Ramella, M. (eds) Large Scale Structure and Motions in the Universe. Astrophysics and Space Science Library, vol 151. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0903-8_19
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