Fractal networks and phase transition in percolation

Networking mechanism in percolation is studied on a square lattice in 2D and on a simple cubic lattice in 3D by means of Monte Carlo technique. The size of the largest clusters increases nonlinearly near the phase-transition point of percolation in the random-scattering process of occupied sites on the lattices. This is caused by the linking mechanism of clusters in the systems. Local dimensionality is defined from magnification rates of mass and of radius for linked clusters The mechanism explains the fractal-growth process of percolation networks.