A Random Multifractal Tilling

Abstract

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 $ρ_i$ related to the section ratio. For the case of random choice between $ρ_1$ and $ρ_2$ we find analytically the full spectrum of fractal dimensions.