We have been studying the two-dimensional continuum percolation problem, using patterns on square cellular structures (square meshes) generated by computer simulation. The metallic critical volume fractions for the metal-insulator transition and the effective conductivities of their patterns agreed well with those of actual materials formed by deposition of metal films on insulator substrates. In this paper we obtain the fractal dimensions of percolation clusters of the two-dimensional continuum percolation models formed by computer simulation, and compare the factal dimensions with the results from the actual experiments of Voss, Laibowitz, and Alessandrini and of Kapitulnik and Deutscher, using transmission electron micrographs of thin metal films deposited on insulator substrates. We clearly show that the fractal properties of percolation clusters on square cellular structures agree well with those of actual experiments. The fractal dimensions are 1.9 for the large percolation clusters occurring when the metallic volume fraction is close to the critical volume fraction for the metal-insulator transition.
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Mitsunobu Nakamura (1986) studied this question.
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