# PlanetPhysics/Catacaustic

Given a plane curve ${\displaystyle \gamma }$, its catacaustic (Greek ${\displaystyle \varkappa \alpha \tau {\acute {\alpha }}\,\varkappa \alpha \upsilon \sigma \tau \iota \varkappa {\acute {o}}\varsigma }$ `burning along') is the envelope of a family of light rays reflected from ${\displaystyle \gamma }$ after having emanated from a fixed point (which may be infinitely far, in which case the rays are initially parallel).
For example, the catacaustic of a logarithmic spiral reflecting the rays emanating from the origin is a congruent spiral. The catacaustic of the exponential curve, ${\displaystyle y=e^{x}}$, reflecting the vertical rays, ${\displaystyle x=t}$, is the catenary ${\displaystyle y=\cosh(x\!+\!1)}$.