  We measure the trajectories of macroscopic magnetic particles pulled against
gravity between twisted alternating magnetic square patterns in a superposed
homogeneous magnetic field normal to both patterns. The two patterns are built
from a set of magentic cubes having a distribution of magnetization. The
magnetic potential between the patterns is a sum of three contributions: two
being periodic on two lattices with different magnitude and orientation, and
the third random contribution arising from the distribution of magnetization of
the cubes. As one varies the twist angle between the two patterns each time the
twist angle coincides with a magic twist angle one of the two periodic lattices
becomes a sublattice of the other lattice. Simulations of particles moving
through patterns with a precise cube magnetization produce pronounced mobility
peaks near magic twist angles that are associated with flat channels. Weak
random fluctuations of the cube magnetization in the experiment and the
simulations cause enhanced random disorder of the potential and reduce the
mobility by scattering particles into the interior of the twisted Wigner Seitz
cells. The mobility undergoes an Anderson transition from magic to generic
behavior as the magnetization disorder increases beyond half of a percent of
the cube magnetization.
