Knight's Tour Golden Star
While making designs on the chessboard with two mini-knight's tour closed circuits, I realized I could construct a complete open knight's tour covering all 64 squares with one circuit that also makes a four-pointed star in the middle of the tour. Check out the following steps I used in making this knight's tour.
Step 1:
I first made a mini-knight's tour consisting of 32 moves, copied it, then rotated it 90 degrees right to make the second mini-knight's tour.
Step 2:
I combined the previous two mini-knight's tours of 32 moves each on one board that ended up making a very nice geometric and symmetrical pattern.
Step 3:
In the following image, I added or replaced the following knight moves with red, orange and black.
Step 4:
In this step, I moved the red line over the top of the orange line, deleted the black line then recolored all the lines in the tour back to blue. This made a single open knight's tour circuit.
Step 5:
I noticed a four-pointed star shape in the middle of the tour and made the following golden star. I changed the background to black and colored all the lines gold to match the star. The first image shows the star with two mini-knight's tour circuits while the second image is a single open knight's tour circuit.
Step 6:
There are many other knight's tours that have the same four-pointed star shape in the middle of their tours. Here are just a few of them. The first one has four mini-knight's tour circuits, the next two have two mini-knight's tour circuits while the last one has one closed knight's tour circuit.