  By using Monte Carlo simulation of pomeron exchange model, the dependence of
the fractal behavior of the pomeron induced system in deep inelastic
lepton-nucleon scattering upon the diffractive kinematic variables is found
rather robust and not sensitive to the distinct parameterization of the pomeron
flux factor and structure function. Based on this characteristic fractal plot,
a feasible experimental test of the phenomenological pomeron-exchange model in
DESY $ep$ collider HERA is proposed.
