  A contact map is a simple representation of the structure of proteins and
other chain-like macromolecules. This representation is quite amenable to
numerical studies of folding. We show that the number of contact maps
corresponding to the possible configurations of a polypeptide chain of N amino
acids, represented by (N-1)-step self avoiding walks on a lattice, grows
exponentially with N for all dimensions D>1. We carry out exact enumerations in
D=2 on the square and triangular lattices for walks of up to 20 steps and
investigate various statistical properties of contact maps corresponding to
such walks. We also study the exact statistics of contact maps generated by
walks on a ladder.
