Semicircles seem excessive. At no point does the wall have an angle over 45 degrees, so a semi-circle which would be at a 90 degree angle for every inflection point seems way too wavy.
A sine wave is probably closer, which would give an arc length of sqrt(1+cos(2pix/L)^2). This has no reasonable closed form I can find but it seems like it would be about 21% longer than a straight line.
Edit: Also a semicircle is pi/2 times as long as its diameter, not pi times.
A right isosceles triangle has a hypotenuse that's √2 (1.41) and 1/√2 = 0.71.
Stack Overflow seems to think it's around 2.4x, but I am not sure I could ever follow the math and I certainly can't now. I think the amplitude makes the difference here and SO is answering a different question, otherwise this article would be wrong and that wasn't my impression the first time I encountered this topic.
second edit: The article linked from this article says:
So a crinkle wall with amplitude 1.4422 uses about as many bricks as a straight wall twice as thick.
A sine wave is probably closer, which would give an arc length of sqrt(1+cos(2pix/L)^2). This has no reasonable closed form I can find but it seems like it would be about 21% longer than a straight line.
Edit: Also a semicircle is pi/2 times as long as its diameter, not pi times.