  We study the $N$ fracton problem in classical mechanics, with fractons
defined as point particles that conserve multipole moments up to a given order.
We find that the nonlinear Machian dynamics of the fractons is characterized by
late-time attractors in position-velocity space for all $N$, despite the
absence of attractors in phase space dictated by Liouville's theorem. These
attractors violate ergodicity and lead to non-equilibrium steady states, which
always break translational symmetry, even in spatial dimensions where the
Hohenberg-Mermin-Wagner-Coleman theorem for equilibrium systems forbids such
breaking. While a full understanding of the many-body nonlinear problem is a
formidable and incomplete task, we provide a conceptual understanding of our
results using an adiabatic approximation for the late-time trajectories and an
analogy with the idea of `order-by-disorder' borrowed from equilibrium
statistical mechanics. Altogether, these fracton systems host a new paradigm
for Hamiltonian dynamics and non-equilibrium many-body physics.
