  We develop the hypothesis that the dynamics of a given system may lead to the
activity being constricted to a subset of space, characterized by a fractal
dimension smaller than the space dimension. We also address how the response
function might be sensitive to this change in dimensionality. We discuss how
this phenomenon is observable in growth processes and near critical points for
systems in equilibrium. In particular, we determine the fractal dimension $d_f$
for the Ising model and validate it via computer simulations for two
dimensions.
