A Random Multifractal Tilling

Details A Random Multifractal Tilling A Random Multifractal Tilling

2004-02-13

arxiv.org/abs/cond-mat/0402372v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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.

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