  We construct a N-dimensional Gaussian landscape with multiscale, translation
invariant, logarithmic correlations and investigate the statistical mechanics
of a single particle in this environment. In the limit of high dimension N>>1
the free energy of the system in the thermodynamic limit coincides with the
most general version of Derrida's Generalized Random Energy Model. The
low-temperature behaviour depends essentially on the spectrum of length scales
involved in the construction of the landscape. We argue that our construction
is in fact valid in any finite spatial dimensions, starting from N=1.
