Numerical calculations of critical densities for lines and planes

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Abstract
Critical percolation densities have been calculated numerically for large systems of lines in two dimensions and planes in three dimensions. Results for lines of varying length have been successfully predicted from the constant length case. In special cases very large systems of up to 1/4 million lines have been studied. By calculating critical densities for a range of system sizes and using a finite-size scaling argument, a prediction of the infinite critical density is made. For the two-dimensional system with fixed length orthogonal lines this corresponds to 3.11 intersections per line. For the three-dimensional system of fixed size orthogonal planes, the prediction is 2.00 intersections per plane.

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