The phase portrait of a typical Hamiltonian dynamical system is a complicated
fractal with strong evidence of
self-similarity. This fractal structure is responsible for the dificulties in the developement of a computationally effective
theory of transport in the phase space. However, the self-similarity of such fractals could be used to encode them in terms
of continuous and smooth functions. This is the basic idea of the method of modular smoothing. We illustrate this method
by discussing its applications for the calculations of KAM tori, critical functions and actions of periodic orbits.