I will present a few results concerning spectral theory of graphs and groups that are based on the use of multidimentional rational maps and self-similar groups. It will be explained how these maps appear, how they help to compute the spectrum, and why they are ''strange'' (or better to say non typical). As part of story there will be a short survey on spectra of infinite graphs and groups with some old and new results belonging to the speaker and his collaborators (L.Bartholdi, A.Dudko, D.Lenz, T.Nagnibeda, B.Simanek, A.Zuk). The relation to the random Schrodinger operator will be mentioned at the end of the talk if time permits.