Fractals and Astronomy

Peebles (1980) states that: "Given a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance." People are also interested in the fractalization of the galaxy distribution in the Universe (out to a certain scale length). Cellular automata uses a fascinating computational technique that can take relatively simple rules to compute phenomena resulting in complex behavior. The figure I created at right is a projection of a 3D set of galaxies projected onto a 2D plane using the stochastic techniques outlined in Vicsek and Szalay (1987).

One can examine the fractal dimension of the simulated image by comparing the number of occupied cells in a grid within a box of size L. The resulting computation is best fit by a power law relation N(L) ~ LD. The least squares fit to the data shown in the figure at right gives a fractal dimension D=1.6. The figure and statistics were created with Mathematica. See the book by Heck and Perdang (1991) for a nice overview of fractal studies in astrophysics.

Interesting topics for study: