I chose to engrave a Hilbert curve because it is a fractal curve that can be multiplied to infinity by drawing a decorative path as it is not monotonic although the basic pattern is very repetitive.
The result looks like a maze but actually this path is the opposite of a maze as it is impossible to get lost. You can visualize it by seeing the video.
Although the entrance is at 2.7 in. (7 cm) from the exit in a straight line the whole route is 25 times longer or about 71 in. (180 cm).