  The past decade has seen a flurry of research into pattern avoiding
permutations but little of it is concerned with their exhaustive generation.
Many applications call for exhaustive generation of permutations subject to
various constraints or imposing a particular generating order. In this paper we
present generating algorithms and combinatorial Gray codes for several families
of pattern avoiding permutations. Among the families under consideration are
those counted by Catalan, Schr\"oder, Pell, even index Fibonacci numbers and
the central binomial coefficients. Consequently, this provides Gray codes for
$\s_n(\tau)$ for all $\tau\in \s_3$ and the obtained Gray codes have distances
4 and 5.
