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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 thedoi:10.1063/1.449215 fatcat:3t7qt7nm4be3nivnw2tyhc33aq