A single-line drawing that is simultaneously an open knight's tour of a 99x99 chessboard and a 3x3 Latin square.
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A knight's tour of a 32x32 chessboard. The knight's path is unicursal. If you start in the lower left corner and follow the path move by move, you will visit each square once and only once and end near the lower right corner. Inspiration: Szpakowski's linear ideas.
"Spiraling to keep myself from spiraling." An open knight's tour of a 99x99 chess board. The tour can be thought of as a tour of 11x11 tours, and it can be extended indefinitely to form an infinite Hamiltonian path through the infinite knight graph. The sky blue arrows help to show the start and end of each 11x11 tour, and the orange line marks the path taken through the 11x11 tours.
An open knight's tour of a 128x128 chessboard. The knight starts in the lower left corner, finishes near the lower right corner, and visits each of the sixteen 32x32 regions in the same order that they'd be visited by a second-stage Hilbert curve. #mathart
A tour of tours, an open knight's tour of a 99x99 chessboard. The tour starts in the bottom left corner and ends near the top right corner. I constructed this tour by selecting two "motif tours" of an 11x11 chessboard (one of them found by the mathematician Éduoard Lucas), arranging them (or their rotations or reflections) into a 9x9 array of 11x11 tours, and then stitching together the 81 11x11 tours with 80 "connectors." The 99x99 tour (the tour of tours) visits the 11x11 chessboard in Peano-curve-like fashion.
A knight's tour proof of a Fibonacci identity.
One line. An interlaced Szpakowski-esque rendering of a Truchet-tile pattern in which the 2x2 blocks are visited in Hilbert-like fashion.
Two knight's tours (32x32 and 64x64). Two terms of an infinite sequence of tours.
Another knight's tour of a 32x32 chessboard. The knight's path is unicursal. If you start in the lower left corner and follow the path move by move, you will visit each square once and only once and end near the lower right corner. Inspiration: Szpakowski's linear ideas.
Another knight's tour of a 32x32 chessboard. The knight's path is unicursal. If you start in the lower left corner and follow the path move by move, you will visit each square once and only once and end near the lower right corner. Inspiration: Szpakowski's linear ideas.
Another knight's tour of a 32x32 chessboard. The knight's path is unicursal. If you start in the lower left corner and follow the path move by move, you will visit each square once and only once and end near the lower right corner. Inspiration: Szpakowski's linear ideas.
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@grwster@mastodon.social Yes, and that would produce a nice 2-factor of the infinite knight graph.
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@yomikoma@weirder.earth I choose to start the tour in a corner and end it in a square diagonally adjacent to a corner in order to be able to stitch together tours so that they make larger tours. Here is an example, a knight's tour proof of a Fibonacci identity.
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@colinliotta@xoxo.zone Yes! They can even be stitched together in Hilbert-curve-like fashion.