  We apply connectedness percolation theory to fractal liquids of hard
particles, and make use of a Percus-Yevick liquid state theory combined with a
geometric connectivity criterion. We find that in fractal dimensions the
percolation threshold interpolates continuously between integer-dimensional
values, and that it decreases monotonically with increasing (fractal)
dimension. The influence of hard-core interactions is only significant for
dimensions below three. Finally, our theory incorrectly suggests that a
percolation threshold is absent below about two dimensions, which we attribute
to the breakdown of the connectedness Percus-Yevick closure.
