  The foundation of the theory presented here has already been proved to be
effective for the case of curves belonging to the Koch family. The present
paper extends the investigation to more complex curves, namely randomly
generated curves and the Weierstrass-Mandelbrot curve. The analysis is focused
on numerical experiments. The results obtained with the numerical analysis
allow advancing some interesting proposition concerning the fine fractal
structure of plane curves. The method uses the dynamical response of
appropriate harmonic oscillators built up according to the geometry of the
fractal set. For the plane motion three fundamental periods are determined.
Each period plotted against the characteristic length of the corresponding
curve in a log-log scale estimates the fractal dimension. It is shown that each
degree of freedom corresponds to a distinct energy covering associate to a
certain topological property. Using this technique it is possible to
distinguish the fine fractal structure of plane curves. The dynamic technique
is proved to work also for the identification problem, that is, to determine
the fractal characteristics embedded in some sample of a given fractal set. It
is proposed the classification of fractal structures into at least two
categories, perfectly fractal and partially fractal. The affine similarity can
be precisely detected using this method.
