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We study electronic properties as a function of the six types of localenvironments found in the octagonal tiling. The density of states has sixcharacteristic forms, although the detailed structure differs from site to sitesince no two sites are equivalent in a quasiperiodic tiling. We present thesite-dependent magnetic susceptibility of electrons on this tiling, which alsohas six characteristic dependences. We show the existence of a non-local spinsusceptibility, which decays with the square of the distance between sites andis the quasiperiodic version of Ruderman-Kittel oscillations. These results areobtained for a tight-binding Hamiltonian with pure hopping.Finally, weinvestigate the formation of local magnetic moments when electron-electroninteractions are included.Comment: 8 pages, LaTeX, figures on reques

Density of states and magnetic susceptibilities on the octagonal tiling