  We consider the Hubbard model for electrons in a two-dimensional
quasiperiodic tiling using the Hartree--Fock approximation. Numerical solutions
are obtained for the first three square approximants of the perfect octagonal
tiling. At half-filling, the magnetic state is antiferromagnetic. We calculate
the distributions of local magnetizations and their dependence on the local
environments as U (Hubbard repulsion strength) is varied. The inflation
symmetry of quasicrystals results in a corresponding inflation symmetry of the
magnetic configurations when passing from one tiling to the next in the
progression towards the infinite quasicrystal.
