  We investigate the effect of noise on Random Boolean Networks. Noise is
implemented as a probability $p$ that a node does not obey its deterministic
update rule. We define two order parameters, the long-time average of the
Hamming distance between a network with and without noise, and the average
frozenness, which is a measure of the extent to which a node prefers one of the
two Boolean states. We evaluate both order parameters as function of the noise
strength, finding a smooth transition from deterministic ($p=0$) to fully
stochastic ($p=1/2$) dynamics for networks with $K\le2$, and a first order
transition at $p=0$ for $K>2$. Most of the results obtained by computer
simulation are also derived analytically. The average Hamming distance can be
evaluated using the annealed approximation. In order to obtain the distribution
of frozenness as function of the noise strength, more sophisticated
self-consistent calculations had to be performed. This distribution is a
collection of delta peaks for K=1, and it has a fractal sructure for $K>1$,
approaching a continuous distribution in the limit $K\gg1$.
