  The dependence of the fractal behaviors 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. A feasible experimental test of the
phenomenological pomeron-exchanged model based on the fractal measurement in
DESY $ep$ collider HERA is proposed.
