Honeycomb Tours

I have added a new page about tours of Honeycomb Boards to the Knight's Tour Notes pages. This collage shows a selection of results. Some date back to 1974 when I sent an example tour to W. Glinski whose Hexagonal Chess on a 91-cell board was popular. Others are new results. I've included wazir, king and knight tours that show various different types of symmetry.

DNA folds into a 3D Wazir Tour!

According to a recent article in Science Daily, or at least the illustration accompanying it, DNA folds into a 3D wazir tour, similar to the 2D examples shown in my drawing alongside. These fractal-type diagrams occur at the end of a section of my Knight's Tour Notes website on Wazir Tours. For those not familiar with the terminology, a "wazir" is a chess piece that moves just to the adjacent square, like a single-step rook, or as in a king's non-diagonal move. A tour of course is a journey or path that visits all the squares of the board once only, without backtracking over any squares already visited.