Scale Dependent Dimension of Luminous Matter in the Universe

We suggest a geometrical model for the distribution of luminous matter in the Universe, where the apparent dimension, $D\left(l\right)$, increases linearly with the logarithm of the scale $l$. Beyond the correlation length, $\xi$, the Universe is homogeneous, and $D=3\mathrm{}$. Comparison with data from the SARS redshift catalog, and the LEDA database provides a good fit with a correlation length $\xi \sim 300$ Mpc. This type of scaling structure was recently discovered in a simple reaction-diffusion “forest-fire” model, indicating a broad class of scaling phenomena.