  We consider a particular class of lattice Schr\"odinger operators with
deterministic potentials depending upon an infinite number of parameters in an
auxiliary measurable space. We prove exponential dynamical localization for
generic families in the strong disorder regime, using a variant of the
Multi-Scale Analysis. In our model, the potential is generated by a function on
a torus which is discontinuous (`haarsh') and constructed with the help of an
expansion which reminds Haar's wavelet expansions.
