Robert (Bob) Bosch @baabbbaash.bsky.social · 13/10/2026All 16 combinations of the four 2-factors, a la Sol LeWitt. 0121
Robert (Bob) Bosch @baabbbaash.bsky.social · 12/10/2026Top left: 2-factor A. Top right: 2-factors A and B. Bottom left: 2-factors A, B, and C. Bottom right: 2-factors A, B, C, and D. Colored with palette 76 from the book “A Dictionary of Color Combinations Vol 2.” 060
Robert (Bob) Bosch @baabbbaash.bsky.social · 11/10/2026Trying another color palette (palette 196 from the book “A Dictionary of Color Combinations Vol 2”) on my favorite decomposition of the infinite knight’s graph into four 2-factors. 0122
Robert (Bob) Bosch @baabbbaash.bsky.social · 11/10/2026Trying another color palette (palette 72 from the book “A Dictionary of Color Combinations Vol 2”) on my favorite decomposition of the infinite knight’s graph into four 2-factors. 1120
Robert (Bob) Bosch @baabbbaash.bsky.social · 10/10/2026Trying a different color palette (palette 76 from the book “A Dictionary of Color Combinations Vol 2”) on my favorite decomposition of the infinite knight’s graph into four 2-factors. 0184
Robert (Bob) Bosch @baabbbaash.bsky.social · 17/08/2026All 16 subsets of the set of the four 2-factors that form the decomposition, a la Sol LeWitt and containing 16x16 sections of the subgraphs. 030
Robert (Bob) Bosch @baabbbaash.bsky.social · 17/08/2026All 16 subsets of the set of the four 2-factors that form the decomposition, à la Sol LeWitt. 130
Robert (Bob) Bosch @baabbbaash.bsky.social · 15/08/2026This is a 24-frame animation of the traversal of a Hamiltonian cycle of the permutohedron (truncated octahedron). Each vertex is one of the 4! = 24 ways of assigning four colors (yellow, blue, black, red) to the four 2-factors that make up the decomposition. 110
Robert (Bob) Bosch @baabbbaash.bsky.social · 14/08/2026Currently, this is my favorite decomposition of the infinite knight’s graph. Note that each of the four 2-factors is a translation of any of the others, and each has mirror symmetry in the downward sloping diagonal. 1120
Robert (Bob) Bosch @baabbbaash.bsky.social · 04/08/2026The same decomposition but with one additional swap (yellow and black). 110
Robert (Bob) Bosch @baabbbaash.bsky.social · 04/08/2026The same decomposition but with yellow and blue swapped. 110
Robert (Bob) Bosch @baabbbaash.bsky.social · 04/08/2026The large image on the right shows a 24x24 section of a decomposition of the infinite knight's graph into four 2-factors The four smaller images on the left show the four 2-factors. Here, the yellow and blue 2-factors are translations of each other, and the same is true for the black and red. 1141
Robert (Bob) Bosch @baabbbaash.bsky.social · 01/08/2026The same decomposition after one additional color swap (yellow and black). 120
Robert (Bob) Bosch @baabbbaash.bsky.social · 01/08/2026Same decomposition, but with yellow and blue swapped. 140
Robert (Bob) Bosch @baabbbaash.bsky.social · 25/07/2026The large image on the right shows a 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The four smaller images on the left show the four individual 2-factors. 1233
Robert (Bob) Bosch @baabbbaash.bsky.social · 05/07/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 090
Robert (Bob) Bosch @baabbbaash.bsky.social · 03/07/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 1170
Robert (Bob) Bosch @baabbbaash.bsky.social · 01/07/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 070
Robert (Bob) Bosch @baabbbaash.bsky.social · 01/07/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 0123
Robert (Bob) Bosch @baabbbaash.bsky.social · 30/06/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 0120
Robert (Bob) Bosch @baabbbaash.bsky.social · 29/06/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 0123
Robert (Bob) Bosch @baabbbaash.bsky.social · 28/06/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 0100
Robert (Bob) Bosch @baabbbaash.bsky.social · 21/06/2026A 24x24 section of a decomposition of the infinite knight's graph into four 2-factors. The vertices are where eight "strands" meet at a point. If you zoom in, you'll see that each vertex has two yellow strands, two blue strands, two black strands, and two red strands. 0103
Robert (Bob) Bosch @baabbbaash.bsky.social · 15/04/2026Cover art for the May 2026 issue of the Notices of the American Mathematical Society. Here's a link to the issue: www.ams.org/notices 63810
Robert (Bob) Bosch @baabbbaash.bsky.social · 12/04/2026A knight's tour solution to a sudoku puzzle. 0152
Robert (Bob) Bosch @baabbbaash.bsky.social · 26/03/2026I converted a text message into a knight's tour. To decode it, follow the knight's tour, starting in the top left corner. The knight will traverse a succession of 11x11 tours, and each of these 11x11 tours corresponds to a letter. The message is a quote from Ursula K. Le Guin. 2164
Robert (Bob) Bosch @baabbbaash.bsky.social · 26/02/2026"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. 0110
Robert (Bob) Bosch @baabbbaash.bsky.social · 28/01/2026A tour of tours, an open knight's tour of an 99x99 chessboard. The tour starts in the bottom left corner and ends near the top right corner. 2287
Robert (Bob) Bosch @baabbbaash.bsky.social · 28/01/2026A single-line drawing that is simultaneously an open knight's tour of a 99x99 chessboard and a 3x3 Latin square. 16720
Robert (Bob) Bosch @baabbbaash.bsky.social · 12/11/2025Two knight's tour (32x32 and 64x64). Two terms of an infinite sequence of tours. 0162
Robert (Bob) Bosch @baabbbaash.bsky.social · 17/08/2025An 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 0192
Robert (Bob) Bosch @baabbbaash.bsky.social · 18/07/2025A 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. #mathart #mathsart #orms #chess 0151
Robert (Bob) Bosch @baabbbaash.bsky.social · 15/07/2025A 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. #mathart #mathsart #orms #chess 0101
Robert (Bob) Bosch @baabbbaash.bsky.social · 14/07/2025A 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. #mathart #mathsart #orms #chess 0110
Robert (Bob) Bosch @baabbbaash.bsky.social · 13/07/2025A 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. #mathart #mathsart #orms #chess 0120
Robert (Bob) Bosch @baabbbaash.bsky.social · 12/07/2025A 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. #mathart #mathsart #orms #chess 1213
Robert (Bob) Bosch @baabbbaash.bsky.social · 11/07/2025A 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. #mathart #mathsart #orms #chess 0101
Robert (Bob) Bosch @baabbbaash.bsky.social · 10/07/2025A knight's tour of a 32x32 chessboard. The knight's path can be traced without lifting one's writing implement from the surface of the paper. Inspiration: Szpakowski's linear ideas. #mathart #mathsart #orms #chess 090
Robert (Bob) Bosch @baabbbaash.bsky.social · 09/07/2025A knight's tour of a 32x32 chessboard. The knight's path can be traced without lifting one's writing implement from the surface of the paper. This tour is close to having 180-degree rotational symmetry and vertical and horizontal mirror symmetries. #mathart #mathsart #chess 0173
Robert (Bob) Bosch @baabbbaash.bsky.social · 08/07/2025A knight's tour of a 32x32 chessboard. The knight's path can be traced without lifting one's writing implement from the surface of the paper. This tour is close to having 180-degree rotational symmetry and vertical and horizontal mirror symmetries. #mathart #chess 070
Robert (Bob) Bosch @baabbbaash.bsky.social · 04/07/2025Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart 0175
Robert (Bob) Bosch @baabbbaash.bsky.social · 03/07/2025Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart 0102
Robert (Bob) Bosch @baabbbaash.bsky.social · 01/07/2025Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart 073
Robert (Bob) Bosch @baabbbaash.bsky.social · 01/07/2025Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart 082