Percolational and fractal property of random sequential packing patterns in square cellular structures

The problem for random packing or filling has been treated in many fields. In this paper we form random sequential packing patterns, filling metallic squares with integer length a on insulator substrates divided into square unit cells. We investigate the percolational and fractal property of the packing patterns, and clarify that the maximum critical percolation length $a_c$ (=3 units length) of the packed squares is presented for the insulator-to-metal transition to take place on the random sequential packing textures. When a>$a_c$, no insulator-to-metal transition occurs even at the saturation coverage where no more squares can be filled without any overlap. However even in such patterns with a>$a_c$, the large percolation clusters possess fractal properties, and the fractal dimensions equal 1.94.