Chatoyancy is a fancy name for a fancy gemstone. Better known as a cat's eye this stone is named for the actions of ...a cat's eye when exposed to light. The line forms an aperture that opens and closes as it is rotated under a direct light source.
Cat's eyes are formed much like a star exception that you have one straight ray instead of six. The light travels down one single direction perpendicular to fiber inclusions in the gemstone which are lined up in the stone. Some of the cat's eye stones like the chrysoberyl cat's eye at the top of this page can be fairly transparent and show a floating eye. In the finer honey colors these can be quite expensive. The cat's eye in the second picture shows a double rayed eye in the open and closed position. The cat's eye emerald at bottom is an excellent example of a gemstone not ordinarily thought to offer this phenomena but is very beautiful if you can find one.