  We introduce fractal liquids by generalizing classical liquids of integer
dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing
the liquid are fractal objects and their configuration space is also fractal,
with the same non-integer dimension. Realizations of our generic model system
include microphase separated binary liquids in porous media, and highly
branched liquid droplets confined to a fractal polymer backbone in a gel. Here
we study the thermodynamics and pair correlations of fractal liquids by
computer simulation and semi-analytical statistical mechanics. Our results are
based on a model where fractal hard spheres move on a near-critical percolating
lattice cluster. The predictions of the fractal Percus-Yevick liquid integral
equation compare well with our simulation results.
