  We perform detailed measurements of the geometrical characteristics of the
percolating cluster of the magnetic monopole currents in the confining phase of
the lattice SU(2) gluodynamics. The Maximal Abelian projection is used to
define the monopoles. The use of the geometrical language is motivated by
recent observations that the full non-Abelian action associated with the
monopoles corresponds to point-like particles on the currently available
lattices. Scaling behavior of various quantities is observed.
