The Kauffman network is a simple model of genetic regulatory networks. The model describes certain general trends among biological organisms such as the relation between the number of cell types of an organism and its gene size. It has been speculated that life, as a complex dynamical system, exists at the edge of chaos. Our analysis and simulation show that the Kauffman network is not only situated at the edge of chaos but also processes complex dynamical behaviors characterized by power-law distributions.