03-3 Jean-Pierre Eckmann, Esa Jarvenpaa, Maarit Jarvenpaa, Itamar Procaccia

On the Fractal Dimension of the Visible Universe (377K, postscript) Jan 2, 03

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Abstract. Estimates of the fractal dimension $D$ of the set of galaxies in the universe, based on ever improving data sets, tend to settle on $D\approx 2$. This result raised a raging debate due to its glaring contradiction with astrophysical models that expect a homogeneous universe. A recent mathematical result indicates that there is no contradiction, since measurements of the dimension of the {\em visible} subset of galaxies is bounded from above by $D=2$ even if the true dimension is anything between $D=2$ and $D=3$. We demonstrate this result in the context of a simple fractal model, and explain how to proceed in order to find a better estimate of the true dimension of the set of galaxies.

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