Check out Greg Egan's new page on caustics! The blue curve here is an ellipse. When we shine light on it, the reflected rays bunch up along a curve called a catacaustic. The ellipse is described by a quadratic equation, but its catacaustic is described by a polynomial equation of degree 6. This is an example of a general pattern discussed by Egan: the catacaustic of a curve of degree d has degree at most 3d(d-1). The math is serious, but the pictures will delight you!
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