  We construct a group acting on a binary rooted tree; this discrete group
mimics the monodromy action of iterates of $f(z)=z^2-1$ on associated coverings
of the Riemann sphere.
  We then derive some algebraic properties of the group, and describe for that
specific example the connection between group theory, geometry and dynamics.
  The most striking is probably that the quotient Cayley graphs of the group
(aka ``Schreier graphs'') converge to the Julia set of $f$.
