  Experiments in various neural systems found avalanches: bursts of activity
with characteristics typical for critical dynamics. A possible explanation for
their occurrence is an underlying network that self-organizes into a critical
state. We propose a simple spiking model for developing neural networks,
showing how these may "grow into" criticality. Avalanches generated by our
model correspond to clusters of widely applied Hawkes processes. We
analytically derive the cluster size and duration distributions and find that
they agree with those of experimentally observed neuronal avalanches.
