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.