We describe an efficient algorithm for computing two-dimensional stable and
unstable manifolds of three-dimensional vector fields. Larger and larger p
ieces of a manifold are grown until a sufficiently long piece is obtained.
This allows one to study manifolds geometrically and obtain important featu
res of dynamical behavior. For illustration, we compute the stable manifold
of the origin spiralling into the Lorenz attractor, and an unstable manifo
ld in zeta(3)-model converging to an attracting limit cycle. (C) 1999 Ameri
can Institute of Physics. [S1054-1500(99)02403-9].