  The famous Laplace's Demon is not only of strict physical determinism, but
also related to the power of differential equations. When deterministically
extended structures are taken into consideration, it is admissible that
fractals are dense both in the nature and in the dynamics. In particular, this
is true because fractal structures are closely related to chaos. This implies
that dynamics have to be an instrument of the extension. Oppositely, one can
animate the arguments for the Demon if dynamics will be investigated with
fractals. To make advances in the direction, first of all, one should consider
fractals as states of dynamics. In other words, instead of single points and
finite/infinite dimensional vectors, fractals should be points of trajectories
as well as trajectories themselves. If one realizes this approach, fractals
will be proved to be dense in the universe, since modeling the real world is
based on differential equations and their developments. Our main goal is to
initiate the involvement of fractals as states of dynamical systems, and in the
first step we answer the simple question "How can fractals be mapped?". In the
present study Julia and Mandelbrot sets are considered as initial points for
the trajectories of the dynamics.
