Isotropic non-crystal fractal systems are generated using the techniqu
e of simulated annealing and frozen Lennard-Jones fluids. From all nea
rest neighbor bonds shorter than 1.15 sigma, a subset is selected rand
omly with the probability p approximate to p(c). Afterwards. bond-perc
olation clusters are searched for. Applying the box-counting method, t
ile fractal dimension D is 2.58 +/- 0.015, and by fitting the slope of
the static structure factor S(q), D is 2.40 +/- 0.02. Both values are
close to that of a fractal system on a three-dimensional lattice.