  We study electronic properties as a function of the six types of local
environments found in the octagonal tiling. The density of states has six
characteristic forms, although the detailed structure differs from site to site
since no two sites are equivalent in a quasiperiodic tiling. We present the
site-dependent magnetic susceptibility of electrons on this tiling, which also
has six characteristic dependences. We show the existence of a non-local spin
susceptibility, which decays with the square of the distance between sites and
is the quasiperiodic version of Ruderman-Kittel oscillations. These results are
obtained for a tight-binding Hamiltonian with pure hopping.Finally, we
investigate the formation of local magnetic moments when electron-electron
interactions are included.
