  We study an antiferromagnetic order in the ground state of the half-filled
Hubbard model on the Penrose lattice and investigate the effects of
quasiperiodic lattice structure. In the limit of infinitesimal Coulomb
repulsion $U \rightarrow +0$, the staggered magnetizations persist to be
finite, and their values are determined by confined states, which are strictly
localized with thermodynamics degeneracy. The magnetizations exhibit an exotic
spatial pattern, and have the same sign in each of cluster regions, the size of
which ranges from 31 sites to infinity. With increasing $U$, they continuously
evolve to those of the corresponding spin model in the $U=\infty$ limit. In
both limits of $U$, local magnetizations exhibit a fairly intricate spatial
pattern that reflects the quasiperiodic structure, but the pattern differs
between the two limits. We have analyzed this pattern change by a mode analysis
by the singular value decomposition method for the fractal-like magnetization
pattern projected into the perpendicular space.
