Amethyst is a type of quartz that is mostly found in geodes and hollow agates. It is composed of silicon dioxide, and scores a 7 on the Mohs hardness scale. From different angles, amethyst occurs in primary hues from a light pinkish violet to a deep purple.
Rutile is a mineral composed primarily of titanium dioxide. Rutile has among the highest refractive indices at visible wavelengths of any known crystal, and also exhibits a particularly large birefringence and high dispersion. Small rutile needles present in gems are responsible for an optical phenomenon known as asterism. Asteriated gems are known as "star" gems. Star sapphires, star rubies, and other "star" gems are highly sought after and are generally more valuable than their normal counterparts.