Dynamics of Invasion Percolation

Simulations of the growth of planar invasion percolation clusters exhibit novel dynamic scaling. The probability to invade a site at a distance r from a reference site at a time t after that site was invaded behaves as N(r,t)=r^-1f(rDt), where D is the fractal dimension of the invaded region. The scaling function has the unusual timing behavior f(u)~uᵃ(u1) and ~u^-b(u1), with a1.4, b0.6, and growth occurring mainly around r~t1/D.