  We study a general model for non-gaussian $1/f$ noise based on an infinite
range quantum Ising spin system in the paramagnetic state, or equivalently,
interacting two-level classical fluctuators. We identify a dilatation
interaction term in the dynamics which survives the thermodynamic limit and
circumvents the central limit theorem to produce non-gaussian noise even when
the equilibrium distribution is that of {\em non-interacting} spins. The
resulting second spectrum (`noise of the noise') itself has a universal $1/f$
form which we analyze within a dynamical mean field approximation.
