Cinnabar dots, better known as "bloodspots" (or "硃砂" in Chinese). They occur when mercury and sulfur are present when the agate was formed. Mercuric sulfide (or cinnabar) is obtained when mercury reacts with sulfur. In its purest form, the color is a deep red. In fact, it is how vermilion pigment is made. However, it is difficult and rare to find it in its purest form in agate. The purest form, used to make vermillion, is usually obtained in labs where conditions can be controlled. In nature, there is usually other material present thus giving it slight variations in its redness.
