Adiabatic and irreversible classical discrete time crystals

We simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along control loop. The conformation three one unit cell adiabatically responds with half frequency creating time crystal at arbitrary low frequency. adiabatic occurs because non-trivial topology stationary manifold. When coupling in different cells, many body effects cause formation topologically isolated crystals dynamical phase transitions between reversible non-adiabatic irreversible space-time-crystallographic arrangements.