  We develop a multifractal random tilling that fills the square. The
multifractal is formed by an arrangement of rectangular blocks of different
sizes, areas and number of neighbors. The overall feature of the tilling is an
heterogeneous and anisotropic random self-affine object. The multifractal is
constructed by an algorithm that makes successive sections of the square. At
each $n$-step there is a random choice of a parameter $\rho_i$ related to the
section ratio. For the case of random choice between $\rho_1$ and $\rho_2$ we
find analytically the full spectrum of fractal dimensions.
