  The truly chaotic finite machines introduced by authors in previous research
papers are presented here. A state of the art in this discipline, encompassing
all previous mathematical investigations, is provided, explaining how finite
state machines can behave chaotically regarding the slight alteration of their
inputs. This behavior is explained using Turing machines and formalized thanks
to a special family of discrete dynamical systems called chaotic iterations. An
illustrative example is finally given in the field of hash functions.
