The first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, and a more detailed view of the universe's large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger. Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2. The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3.

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The universe has been observed to be homogeneous and isotropic (i.e. is smoothly distributed) at very large scales, as is expected in a standard Big Bang or Friedmann-Lemaître-Robertson-Walker cosmology, and in most interpretations of the Lambda-Cold Dark Matter model. The scientific consensus interpretation is that the Sloan Digital Sky Survey (SDSS) suggests that things do indeed smooth out above 100 Megaparsecs.

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One study of the SDSS data in 2004 found "The power spectrum is not well-characterized by a single power law but unambiguously shows curvature ... thereby driving yet another nail into the coffin of the fractal universe hypothesis and any other models predicting a power-law power spectrum".Another analysis of luminous red galaxies (LRGs) in the SDSS data calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 Mpc/h) at 3, consistent with homogeneity, but that the fractal dimension is 2 "out to roughly 20 h−1 Mpc. In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 7Mpc/h.

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- Wikipedia 'Fractal Cosmology' Mar 2021