M-O-D-U-L-A-R Knight's Tours

Another fun and easy way to create Knight's Tours is M-O-D-U-L-A-R. Break down an 8x8 square chess board into smaller rectangles such as two 3x4 and two 4x5 rectangles. To create open and closed Knight's Tours, only five simple patterns should be learnt. When using rotation or reflection, only two patterns are actually needed to complete an open Knight's Tour.

Modular Knight's Tour by Dan Thomasson, February 15, 2005

See a simple 2x3x4 Closed Knight's Tour using the 3x4 module B previously listed. The following Closed Knight's Tour, created in Bryce 5.0, is encapsulated within 64 glass cubes. It shows the same 8x8 modular Closed Knight's Tour as above.

8x8 Closed Modular Knight's Tour in Glass By Dan Thomassom, February 22, 2005

I just noticed (April 29, 2007) in the 1917 publication of Amusements in Mathematics by Henry Ernest Dudeney, that Henry shows a similar, but slightly different, modular Knight's Tour as the Closed Knight's Tour shown above. On page 103, Henry presents the modular Knight's Tour puzzle (#338 - The Board in Compartments) with the following solution shown on page 229.

The same M-O-D-U-L-A-R design for creating 2d 8x8 Knight's Tours, can be used to create 3d 8x8x8 cubic Knight's Tours. The following graphic shows all eight 8x8 levels of an 8x8x8 cube. The Knight's Tour starts on the first level with the highlighted green square. The last Knight's move on level 1 is shown with a highlighted dark grey square that connects to the dark grey square on level 2. As the Knight moves from level to level, dark grey squares connect to dark grey squares while light grey squares connect to light grey squares.

The following graphic shows the expected Top-Down view of the 3d Cubic Open Knight's Tour.

Here is the actual Top-Down view of all eight layers of the 3d Cubic Open Knight's Tour created in Bryce 5.0.

3d Cubic Open Knight's Tour

Enjoy the following nine pictures of the 3d Cubic Open Knight's Tour that I also designed in Bryce 5.0. The nine pictures are copyrighted © February 22 2005 by me. I spaced the levels slightly further apart for better viewing.

3d Cubic Open Knight's Tour by Dan Thomasson, February 22, 2005

3d Cubic Open Knight's Tour - Front View

3d Cubic Open Knight's Tour - Right Side View

3d Cubic Open Knight's Tour - Inside View

3d Cubic Open Knight's Tour - Top-down View

3d Cubic Open Knight's Tour - Top-down Corner Angle View

3d Cubic Open Knight's Tour - Top-down Front Angle View

3d Cubic Open Knight's Tour - Center-front Angle View

3d Cubic Open Knight's Tour - Center-Side Angle View

The 3x4 M-O-D-U-L-A-R Knight's Tour patterns "A" and "B" can also be used to make nice picture frame borders, borders around web-pages, or trim around walls. See the following Closed Knight's Tour border sample. To increase the size of the frame or border, insert additional module "B" patterns between the module "A" patterns.