Abstract
The study of random fractals on d-dimensional hypercubic space enables us to define ( d − 1) classes of percolating structures in these fractals. Such percolating structures are shown here when d = 2 and d = 3. The fractal dimensions of these sets at the percolation thresholds are: 3 2 for d = 2 corresponding to a threaded structure, and 2 and 8 3 for d = 3, corresponding respectively to a threaded structure and a twisted structure. The study of random walk on these percolating structures reveals the harmonic analysis of electrical and transport properties.
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