  In this article, we extend the idea of stochastic dyadic Cantor set to
weighted planar stochastic lattice that leads to a stochastic porous lattice.
The process starts with an initiator which we choose to be a square of unit
area for convenience. We then define a generator that divides the initiator or
one of the blocks, picked preferentially with respect to their areas, to divide
it either horizontally or vertically into two rectangles of which one of them
is removed with probability $q=1-p$. We find that the remaining number of
blocks and their mass varies with time as $t^{p}$ and $t^{-q}$ respectively.
Analytical solution shows that the dynamics of this process is governed by
infinitely many hidden conserved quantities each of which is a multifractal
measure with porous structure as it contains missing blocks of various
different sizes. The support where these measures are distributed is fractal
with fractal dimension $2p$ provided $0<p<1$. We find that if the remaining
blocks are characterized by their respective area then the corresponding block
size distribution function obeys dynamic scaling.
