  Artificial spin ice (ASI) are nanomagnetic metamaterials exhibiting a wide
range of emergent properties, which have recently shown promise for
neuromorphic computing. However, the lack of efficient protocols to control the
state evolution of these metamaterials has been limiting progress. To overcome
this barrier, we introduce astroid clocking, a global field protocol offering
discrete, gradual evolution of spin states. The method exploits the intrinsic
switching astroids and dipolar interactions of the nanomagnets to selectively
address ASI spins in sequence. We demonstrate, experimentally and in
simulations, how astroid clocking of pinwheel ASI allows ferromagnetic domains
to be gradually grown or reversed at will. More complex dynamics arise when the
clock protocol allows both growth and reversal to occur simultaneously. Astroid
clocking offers unprecedented control and understanding of ASI dynamics in both
time and space, extending what is possible in nanomagnetic metamaterials.
