Clothoid

The curve whose curvature rises in step with its length, so that it winds ever tighter toward two points it never reaches. Roads and railways use it to pass from a straight into a bend without a jolt. Cornu drew it in 1874 to read the diffraction of light off a graph.

x = ∫₀ᴸ cos(s²) ds, y = ∫₀ᴸ sin(s²) ds

On mathcurve.com as Spirale de Cornu ou clothoïde