Thomas Jefferson famously incorporated serpentine walls into the architecture of the University of Virginia. Although on some accounts he invented that design—Wikipedia, for instance, calls them "uniquely Jeffersonian"—it in fact appears that he at best improved on the "crinkle-crankle" walls that he had admired in England. We can at least give Jefferson credit for boldness in borrowing good ideas. The serpentine wall economizes on bricks despite its meandering path because, in contrast to a straight wall, it can be made merely one brick thick. A straight wall so thin would topple easily, whereas the curves of a serpentine wall help it to resist lateral forces. You can see Jefferson's design in his own hand, here.
I've come up with a variation on the serpentine wall used by Jefferson, one that improves that original in several ways. Jefferson's serpentine wall has vertical faces throughout its length. I propose, in contrast, a wall that leans in from a wide base towards a narrow top. In other words, the base of my wall would follow a larger amplitude sine curve than would its top. (The base and top curves would run in phase.) Here's a sketch.
Why do I propose that design? Three reasons: Compared to Jefferson's wall, my design would 1) further economize on materials; 2) look more interesting and attractive; and 3) make the wall still more resistant to lateral forces.
The first point needs little elaboration. If the top of the wall follows a less wending line than the base, it will use less material. I cannot really prove the second point; it speaks to matters of taste. I will observe, though, that my wall at least offers the aesthetic virtues of originality.
The third point perhaps needs explaining. Jefferson's design has this virtue: The wall as a whole offers greater resistance to lateral forces than a conventional, straight wall does. Note, though, that individual portions of Jefferson's design may under-perform a conventional wall. Consider his wall not as a whole, but segments of arc length pi/2. (Why consider wall segments? Because masonry walls prove stronger in compression than tension, meaning they may pull apart under lateral forces.)
A short segment of Jefferson's wall offers improved strength only to lateral forces applied toward the convex sides of the wall's curves. To lateral forces applied to the concave sides of its curves, it offers even less resistance than a conventional, straight wall. My wall, in contrast, would offer increased resistance to lateral forces applied at both convex and concave points. I'll skip an engineering analysis, since the reasons should be apparent on reflection. Don't get it? Try thinking about how a force pressing against a inward-leaning section of my wall would have to lift the bricks to displace them.
That said, I recognize that my design presents some challenges. For one thing, it would probably require a specially-designed foundation, one canted at various angles at various points. For another thing, my wall would call for some complicated masonry—not the usual regular, vertical sort. Portions would lean, making brick-laying a challenge. It would help to lay the vertical portions first and then build the portions in between, as you would an arch.
A last challenge: Because the arc length of the wall would be shorter at its top than at its bottom, alternate courses of uniform brick would not line up neatly, with one row's divisions centered on the adjoining rows' bricks. That admits various cures. You could leave wider spaces between the lowest bricks, for instance, leaving the masonry complicated but not impossible. Or your could use something other than masonry, such as flexible chain link, overlapping boards, or poured concrete.
Would those problems, taken together, render my version of a serpentine wall wholly infeasible? I don't think so, but I cannot say that I know. I'd love to have a demo of my design built, to see how it works in practice. Toward that end, I'm running the idea past the architect working on our current remodeling project. He'll probably talk me out if it, the sensible fellow. Maybe I should, like Jefferson, start my own university. Institutions of higher learning seem to like nutty architecture.