  We study the space of all compact structures on a two-dimensional square
lattice of size $N=6\times6$. Each structure is mapped onto a vector in
$N$-dimensions according to a hydrophobic model. Previous work has shown that
the designabilities of structures are closely related to the distribution of
the structure vectors in the $N$-dimensional space, with highly designable
structures predominantly found in low density regions. We use principal
component analysis to probe and characterize the distribution of structure
vectors, and find a non-uniform density with a single peak. Interestingly, the
principal axes of this peak are almost aligned with Fourier eigenvectors, and
the corresponding Fourier eigenvalues go to zero continuously at the
wave-number for alternating patterns ($q=\pi$). These observations provide a
stepping stone for an analytic description of the distribution of structural
points, and open the possibility of estimating designabilities of realistic
structures by simply Fourier transforming the hydrophobicities of the
corresponding sequences.
