Knight's Tour Open Circuit V
While making designs on the chessboard with four mini-knight's tour open circuits, I realized I could construct a complete semi-magic knight's tour covering all 64 squares with one circuit. Check out the following steps I used in making the knight's tour.
Step 1:
I first made one complete circuit consisting of 16 moves in blue then copied the circuit and flipped it vertically to make the second circuit and colored the moves red.
Step 2:
I then flipped the first two circuits horizontally and colored the moves green and orange respectively.
Here are the same four 16-move mini-knight tours in blue, red, green and orange.
Step 3:
I combined all four mini-knight's tours on one board that ended up making a very nice geometric and symmetrical pattern. The next image shows the same pattern with two closed 32 knight-move circuits.
Step 4:
After combining all four mini-knight's tours, I wanted to keep most of the symmetrical pattern but make a single 64 move knight's tour. I was able to do this by moving only one line (knight move) and deleting one line. In the following image, I colored all the moves blue. Next, I added red, orange, and black lines.
Step 5:
In this step, I moved the red line over the top of the orange line, and deleted the black line then recolored all the lines in the tour back to blue.