Would it be stronger for the same amount of bricks if it didn't have the inflection point where there is no curvature, and instead had intersecting arcs like: ︾︾︾︾
?
I think it would be less strong than a wavy wall of similar brick count, but still more efficient than an equivalent strength wall built in a straight line.
My mental reasoning for this is that a (pseudo) sinusoid spends a lot more of its path further away from the centre. Thinking of it as a point moving along the path through time, it will dwell and the peaks, and cruise through he centre. The contribution of each brick to wall stiffness will be related to the cube of the distance from the centre line (neutral axis), so more 'time' spent at the peaks is best. This holds true on the macro scale, but could vary on the scale of a half 'wavelength' as the lack of inversion of curvature could be beneficial there.
Everything moderately reasonable seems to be better than a straight line in this instance. In the limit, two much thinner walls, far apart, is the optimal solution, but that becomes unreasonable as those walls must be coupled together to provide strength.
I think you're asking if a series of arcs is stronger than a wavy line. It's a great question and I think the answer to that would require a full model of the two walls to calculate all the stresses, etc. But I think it would also depend on the question of "stronger against what?" A pushing force but at what point and at what angle. Even height might make a difference.
My gut instinct is that the point where a wavy wall changes from curving one way to another is a slight weak point and perhaps an angle there would actually be stronger. Might be totally wrong.
If you made the arcs deeper than the curves of the wave I think yes. If you just sliced and flipped the arcs from the original wave, no. It'd be a straightforward calculation for the moment of inertia but I'm too lazy to do it. It's all about placing the most mass farthest from the centroid line.
