  We have created and studied artificial magnetic quasicrystals based on
Penrose tiling patterns of interacting nanomagnets that lack the translational
symmetry of spatially periodic artificial spin ices. Vertex-level degeneracy
and frustration induced by the network topology of the Penrose pattern leads to
a low energy configuration that we propose as a ground state. Topologically
induced emergent frustration means that this ground state cannot be constructed
from vertices in their ground states. It has two parts, a quasi-one-dimensional
rigid "skeleton" that spans the entire pattern and is capable of long-range
order, and "flippable" clusters of macrospins within it. These lead to
macroscopic degeneracy for the array as a whole. Magnetic force microscopy
imaging of Penrose tiling arrays revealed superdomains that are larger for more
strongly coupled arrays. The superdomain size is larger after
AC-demagnetisation and especially after annealing the array above its blocking
temperature.
