  We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional
bipartite quasiperiodic structure, the octagonal tiling -- the aperiodic
equivalent of the square lattice for periodic systems.
  An approximate block spin renormalization scheme is described for this
problem. The ground state energy and local staggered magnetizations for this
system are calculated, and compared with the results of a recent Quantum Monte
Carlo calculation for the tiling. It is conjectured that the ground state
energy is exactly equal to that of the quantum antiferromagnet on the square
lattice.
