  A closed plane meander of order n is a closed self-avoiding loop 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. This
allows us to calculate the number of closed meanders up to n=24. The algorithm
is easily modified to enumerate various systems of closed meanders,
semi-meanders or open meanders.
