Fractals in isotropic systems generated with attracting spheres

Isotropic non-crystal fractal systems are simulated. Lennard-Jones fluids are heated up to very high temperatures and annealed to frozen glassy or amorphous states. From the set of all connections between next neighbors separated by less than 1.15σ, a subset is selected randomly with the probability p≈pc. With these bonds the percolation cluster is determined, and all particles not belonging to this cluster are removed. A fractal dimension D≈2.58 is determined using the box-counting method. Considering the slope of the statis structure factor S(q), D is ≈2.40. Both values are close to the ones of a fractal system on a three-dimensional lattice but larger than the fractal dimension D = 1.7 of a recent small angle neutron scattering experiment of base-catalyzed silica aerogels.