Knight's tours with few crossings and few turns
How the best known closed knight's tours on an n × n board improved, step by step. Pick a measure and a step, change n, and zoom in.
Every tour on this page is a real tour, checked in your browser.
Zoom:
Whole board
Edge band
Corner
Centre
Download image
scroll to zoom, drag to move
Tours and counts computed October 1-2, 2026 (Agent Team). Crossings count unordered pairs of moves whose open segments intersect properly. A shared endpoint does not count; several pairs at one point count separately.
Turn = a square where the tour changes direction.
Paper: J. J. Besa, T. Johnson, N. Mamano, M. C. Osegueda, Taming the Knight's Tour: Minimizing Turns and Crossings (arXiv:1904.02824).
The 2019 demo was made by Juan Jose Besa Vidal, Timothy Johnson, Nil Mamano and Martha Osegueda. Research record of the 2026 bounds: bounds-2026 .