A closed plane meander of order n is a closed self-avoiding curve
intersecting an infinite line 2n times. Meanders are considered distinct up
to any smooth deformation leaving the line fixed. We have developed an improved
algorithm, based on transfer matrix methods, for the enumeration of plane
meanders. While the algorithm has exponential complexity, its rate of growth is
much smaller than that of previous algorithms. The algorithm is easily modified
to enumerate various systems of closed meanders, semi-meanders, open meanders
and many other geometries.Comment: 13 pages, 9 eps figures, to appear in J. Phys.