all gemstones are composed of crystals. amethyst - rather, the chemical broth that crystallizes into amethyst - grows in layers almost like a tree's rings, and in some cut stones this is very prominent and can be seen when you put the stones face down on a brilliantly reflective surface. the layers are termed lamellae just like the lamellae on the underside of a common field mushroom, except that they are alternating layers of left- and right-handed quartz.
(it is easier for non-gemmologists or neophytes to see the layers this way altho they can be seen looking into the stone with a proper loupe)
there is also a stone called "ametrine" which is purple and yellow-yellowish orange. in that case there is an intergrowth of citrine and amethyst (first cousins) that is visible because the layers are large enough to be seen with the eye only.
and not to forget when one is looking at modern jewellery:
almost all modern amethyst has been cooked. that is to say it is heated un a very hot furnace to the point where the colour is a richer, more intense purple. and depending on the temperature and length of exposure, one can turn an amethyst (a pale, tired-looking, or grossly-banded stone) into a citrine or - the current vogue - a green amethyst.
the necklace in question is an older one and i would be surprised if those stones had been cooked.