  We study numerically the magnetic properties (magnetization and
magnetoresistance) of ultra-thin magnetic films (Fe/Cr) grown following the
Fibonacci sequence. We use a phenomenological model which includes Zeeman,
cubic anisotropy, bilinear and biquadratic exchange energies. Our physical
parameters are based on experimental data recently reported, which contain
biquadratic exchange coupling with magnitude comparable to the bilinear
exchange coupling. When biquadratic exchange coupling is sufficiently large a
striking self-similar pattern emerges.
