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[Abstract = "Properties of some chaotic fractal models constructed on hierarchies of rectangular cells (the latter being rectangular subsets of the square lattice) are investigated. Fractal dimensionalities and Lx x Ly (2 ≤ Lx ≤4, 1 ≤ Ly ≤ 4) are derived. Generating probability functions and critical indices for the correlation length as well as for the percolation cluster density are calculated for the models considered. The calculations show that structures generated by anisotropic (rectangular) initial cells show much broader range of critical indices and other characteristic parameters than structures generated by 'isotropic' (square) initial cells."]