Amethyst is the purple variety of quartz, and the colour comes from iron substituting for silicon in the crystal lattice — along with natural radiation over long periods, which is what makes the colour stable. Heated above about 400 °C it turns yellow, which is where citrine comes from.
On a natural strand the tone varies, because the iron content is not constant through a crystal. Uniformly deep purple beads at a low price are usually either very small or treated; natural amethyst of good colour is one of the more expensive quartz varieties.