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The authors calculate the fractal dimension d(min) of the shortest path l between two points on a percolation cluster, where l approximately rd(min) and r is the Pythagorean distance between the points. They find d(min)=1.130+or-0.002 for d=2 and 1.34+or-0.01 for d=3.
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Herrmann et al. (1988) studied this question.
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