caustic optics

Each brilliant point is a specular image of the sun in the water, and corresponds to a critical point in the distance sun-water-eye. Over time, the water surface changes as the waves move, and these points are born or annihilate in pairs. At such a ‘twinkle’ the water surface is not only oriented to reflect light into the eye but is curved so as to focus it there. This interaction of two critical points, as a single parameter (time) varies, is the simplest catastrophe, called the fold. Another familiar fold is the rainbow, where the single parameter is the deflection angle of sunrays to raindrops.