The Fractal Nature of the Universe

Paul Coleman

Many examples of fractal geometry are seen in the field of Astronomy,
from nearby objects such as our Sun, to phenomena at intermediate length
scales in our Galaxy such as the distribution of masers.  This talk will
concentrate on the largest scales which can be probed in our universe,
analyses of locations of galaxies.  It has been known for some twenty
years that the distribution of galaxies on small scales is fractal. 
This is seen in analyses which indicate that both galaxies and their
clusters are power law correlated (a signature of fractal behavior).  At
larger length scales the distribution is supposed to exhibit a so-called
correlation length and was thought to then become homogeneous - except
for occasional fluctuations.  More data and subsequent analysis has
shown that these fluctuations are anything but occasional, as structures
are seen to exist on length scales up to the maximum scales which can be
probed with the new data.  By reanalyzing the data, with methods that
are particularly suited to fractal distributions, one finds no
correlation length at all - indicating that the fractal structure may
extend up to perhaps the largest length scales possible.  Analysis also
indicates that when galaxy masses are considered, the distribution may
be multi-fractal.  These conclusions have serious implications for many
sub-fields in astrophysics today, from galaxy formation to the
Robertson-Walker metric of spacetime.