  We investigate a class of weighted planar stochastic lattice (WPSL1) created
by random sequential nucleation of seed from which a crack is grown parallel to
one of the sides of the chosen block and ceases to grow upon hitting another
crack. It results in the partitioning of the square into contiguous and
non-overlapping blocks. Interestingly, we find that the dynamics of WPSL1 is
governed by infinitely many conservation laws and each of the conserved
quantities, except the trivial conservation of total mass or area, is a
multifractal measure. On the other hand, the dual of the lattice is a
scale-free network as its degree distribution exhibits a power-law $P(k)\sim
k^{-\gamma}$ with $\gamma=4.13$. The network is also a small-world network as
we find that (i) the total clustering coefficient $C$ is high and independent
of the network size and (ii) the mean geodesic path length grows
logarithmically with $N$. Besides, the clustering coefficient $C_k$ of the
nodes which have degree $k$ decreases exactly as $2/(k-1)$ revealing that it is
also a nested hierarchical network.
