  We describe extensive computational experiments on spectral properties of
random objects - random cubic graphs, random planar triangulations, and Voronoi
and Delaunay diagrams of random (uniformly distributed) point sets on the
sphere). We look at bulk eigenvalue distribution, eigenvalue spacings, and
locality properties of eigenvectors. We also look at the statistics of
\emph{nodal domains} of eigenvectors on these graphs. In all cases we discover
completely new (at least to this author) phenomena. The author has tried to
refrain from making specific conjectures, inviting the reader, instead, to
meditate on the data.
