  Critical, or scale independent, systems are so ubiquitous, that gaining
theoretical insights on their nature and properties has many direct
repercussions in social and natural sciences. In this report, we start from the
simplest possible growth model for critical systems and deduce constraints in
their growth : the well-known preferential attachment principle, and, mainly, a
new law of temporal scaling. We then support our scaling law with a number of
calculations and simulations of more complex theoretical models : critical
percolation, self-organized criticality and fractal growth. Perhaps more
importantly, the scaling law is also observed in a number of empirical systems
of quite different nature : prose samples, artistic and scientific
productivity, citation networks, and the topology of the Internet. We believe
that these observations pave the way towards a general and analytical framework
for predicting the growth of complex systems.
