The Kauffman net is a dynamical system of logical variables receiving
two random inputs and each randomly assigned a Boolean function. We sh
ow that the attractor and transient lengths exhibit scaleless behavior
with power-law distributions over up to 10 orders of magnitude in pro
bability. Our results provide evidence for the existence of the ''edge
of chaos'' as a distinct regime between the ordered and chaotic phase
s analogous to a critical point in statistical mechanics. The power-la
w distributions are robust to the changes in the composition of the tr
ansition rules and network dynamics.