There's a study of "meanders"—think a river that starts in the southwest, crosses a road n times, then flows eastward. It's related to the stamp folding problem (the end stamps have to point "outward"...) The sequence begins 1, 1, 2, 3, 8... https://oeis.org/A005316
It turns out that the nth meander number is the number of circular labyrinths (of the specific type shown below) with n circular walking paths.