Knight's Tour with 180 Degrees Rotation Symmetry III
While making designs on the chessboard with two mini-knight's tour closed circuits, I realized I could construct a complete closed knight's tour covering all 64 squares with one circuit that has 180 degrees rotation symmetry. Check out the following steps I used in making this knight's tour.
Step 1:
I first made one complete circuit consisting of 32 moves then copied the circuit and rotated it 90 degrees right to make the second circuit.
Step 2:
I combined both mini-knight's tours on one board that ended up making a very nice geometric and symmetrical pattern.
Step 3:
After combining the two mini-knight's tours, I wanted to keep most of the symmetrical pattern but make a single 64 move closed knight's tour. In the following image, I added or replaced the following knight moves with red, orange, yellow, green, lavender and aqua blue colors.
Step 4:
In this step, I moved the red lines over the top of the orange lines, yellow over to green, lavender to aqua blue, then recolored all the lines in the tour back to blue. The following single closed circuit has 180 degrees rotational symmetry (either horizontally or vertically).