  We introduce a random bit-string model of post-transcriptional genetic
regulation based on sequence matching. The model spontaneously yields a scale
free network with power law scaling with $ \gamma=-1$ and also exhibits
log-periodic behaviour. The in-degree distribution is much narrower, and
exhibits a pronounced peak followed by a Gaussian distribution. The network is
of the smallest world type, with the average minimum path length independent of
the size of the network, as long as the network consists of one giant cluster.
The percolation threshold depends on the system size.
