  A discrete time crystal is a remarkable non-equilibrium phase of matter
characterized by persistent sub-harmonic response to a periodic drive.
Motivated by the question of whether such time-crystalline order can persist
when the drive becomes aperiodic, we investigate the dynamics of a
Lipkin-Meshkov-Glick model under quasiperiodic kicking. Intriguingly, this
infinite-range-interacting spin chain can exhibit long-lived periodic
oscillations when the kicking amplitudes are drawn from the Thue-Morse sequence
(TMS). We dub this phase a ``self-ordered time crystal" (SOTC), and demonstrate
that our model hosts at least two qualitatively distinct prethermal SOTC
phases. These SOTCs are robust to various perturbations, and they originate
from the interplay of long-range interactions and the recursive structure of
the TMS. Our results suggest that quasiperiodic driving protocols can provide a
promising route for realizing novel non-equilibrium phases of matter in
long-range interacting systems.
