  In this article we study the dynamics generated by germs of parabolic
diffeomorphisms f : (C; 0)->(C; 0) tangent to the identity. We show how formal
classification of a given parabolic diffeomorphism can be deduced from the
asymptotic development of what we call directed area of the
epsilon-neighborhood of any orbit near the origin. Relevant coefficients and
constants in the development have a geometric meaning. They present fractal
properties of the orbit, namely its box dimension, Minkowski content and what
we call residual content.
