We perform random walk simulations on binary three-dimensional simple cubic lattices covering the entire ratio of open/closed sites (fractionp) from the critical percolation threshold to the perfect crystal. We observe fractal behavior at the critical point and derive the value of the number-of-sites-visited exponent, in excellent agreement with previous work or conjectures, but with a new and imprOVed computational algorithm that extends the calculation to the long time limit. We show the

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... over to the classical Euclidean behavior in these lattices and discuss its onset as a function of the fractionp. We compare the observed trends with the two-dimensional case.