  We study domain growth dynamics when the target state is suddenly changed on
all length scales. This procedure mimics the `chaos' effect postulated by the
droplet theory of spin-glasses, and allows us to investigate in details its
various dynamical consequences. We study the problem by a variety of methods,
including scaling arguments, analytical solution of the spherical Mattis model,
and Monte Carlo simulations of a 2-dimensional Ising Mattis model. We show that
successive coarsening with respect to different equilibrium states imprints
multiple domain structures on top of each other, plus extra noise due to random
interferences. We demonstrate that the domain structures can be retrieved by an
additional series of coarsening in the reversed order which removes the noises.
We discuss the rejuvenation (chaos) and memory effects observed in
temperature-cycling experiments in glassy systems from the present point of
view, and discuss some open problems and alternative descriptions.
