  We investigate a new model of binary fragmentation with inhibition, driven by
the white noise. In a broad range of fragmentation probabilities, the power-law
spatiotemporal correlations are found to arise due to self-organized
criticality (SOC). We find in the SOC phase a non-trivial power spectrum of the
temporal sequence of the fragmentation events. The $1/f$~ behaviour is
recovered in the irreversible, near-equilibrium part of this phase.
