Every closed meander whose lower arcs form a rainbow appears here exactly once. To make the children of a meander, cut one of its outermost upper arcs and swing the two loose ends down around the whole picture, where they close up as a new outer rainbow arc. A meander with k outermost upper arcs has k children. The new arc is drawn in red.
z² folds every node: the river closes up into a ray from a source (dot) and each node becomes its semi-meander. M picks out the honest meanders and dims the rest: no upper arc crosses the centre, so folding gives a closed meander of half the order. Every meander appears exactly once this way, at even orders.
Drag to pan, scroll or pinch to zoom. Pan down and the tree grows under whatever you are looking at. Tap a meander to inspect it.
z² folds each node into its semi-meander; M picks out the genuine meanders, which fold to meanders of half the order.
Each meander's children come from cutting one of its outermost upper arcs and swinging the two ends down around everything, closing up as a new outer rainbow arc (red). Every rainbow meander appears exactly once.
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The totals are the semimeander numbers.