  In this article we study how a subshift can simulate another one, where the
notion of simulation is given by operations on subshifts inspired by the
dynamical systems theory (factor, projective subaction...). There exists a
correspondence between the notion of simulation and the set of forbidden
patterns. The main result of this paper states that any effective subshift of
dimension d -- that is a subshift whose set of forbidden patterns can be
generated by a Turing machine -- can be obtained by applying dynamical
operations on a subshift of finite type of dimension d + 1 -- a subshift that
can be defined by a finite set of forbidden patterns. This result improves
Hochman's [Hoc09].
