# Why does sunlight on these windows form caustics with a seemingly hyperbolic pattern?

I noticed these caustics outside my office about a month ago and took pictures: one facing towards the sun and one facing towards the reflective surface (a set of double-paned windows).

The seemingly-hyperbolic form of these caustics really captured my attention, and in searching I stumbled on catastrophe theory. Apparently there are seven types of catastrophe (for systems with less than four variables.)

I'd really like to learn more about how these kinds of patterns are generated, but I don't know how to get started with the math. Can anyone explain what type of catastrophe that would result in this pattern?

• Are the windows flat? As I see them they are not flat, but they are like a bowl. They are bent in or outwards? – Árpád Szendrei Mar 29 '19 at 20:50
• I don't recall that they were curved when I looked at them up close, but I do think you're right: in the left image the horizon forms a upward-facing "U" shape, which suggests to me that the outer window was (at the time) a slightly concave 'bowl-like' shape. – D. Betchkal Mar 29 '19 at 23:41