Knight's Tour
​ Closed Construction III

While making designs on the chessboard with two mini-knight's tour closed circuits of 32 moves each, I realized I could construct a complete closed 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 32 moves then copied the circuit and flipped it vertically to make the second circuit.

Step 2:

I combined the two mini-knight's tours on one board that ended up making a very nice symmetrical and geometric pattern.  I show the two separate 32 move circuits in the second image with blue and red lines.

Step 3:

After combining the two mini-knight's tours, I wanted to make a single 64 move closed knight's tour.  I was able to do this by adding or replacing different colored lines to some of the knight's moves on the board.   I used red, orange, yellow and green colors for the lines.  

Step 4:

In this step, I moved the red line (knight's move) to the orange line and yellow to green then recolored all the lines in the tour back to blue.  Here is the single closed knight's tour made by only moving two lines.