Invasion percolation into a percolating cluster

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Abstract
Results are presented for two-dimensional invasion-percolation simulations into percolating clusters. The fractal dimensions of the invading clusters are calculated for different occupation fractions. If the percolating cluster is above the percolation threshold, the fractal dimension is 1.81. On the other hand, if the percolating cluster is at the percolation threshold, the fractal dimension of the invading cluster is approximately 1.37. At threshold the invading cluster is formed exclusively of links and dead ends. If the dead ends are suppressed, the fractal dimension of the object is virtually 1.20, which is close to the fractal dimension of the minimum path between two points connected by the backbone.