Eh, I am a geoscientist (mineralogist), but I'll try to be as un-nerdy as possible in my answer... Amethyst is a kind of quartz. The purple color results from iron and irradiation, which does interesting things to the crystal lattice. Quartz is found basically everywhere, so I guess the question is only where you get the conditions to turn it purple. The pretty quartz, with the large distinct crystals of gem-like quality, is usually hydrothermal. It's found in... bubbles (druses) in volcanic rock, where fluids went through and left the SiO2 behind. So you'd need a volcanic rock that contains iron... ...eh, how much geological detail do you need? XD
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Amethyst is a kind of quartz. The purple color results from iron and irradiation, which does interesting things to the crystal lattice. Quartz is found basically everywhere, so I guess the question is only where you get the conditions to turn it purple.
The pretty quartz, with the large distinct crystals of gem-like quality, is usually hydrothermal. It's found in... bubbles (druses) in volcanic rock, where fluids went through and left the SiO2 behind. So you'd need a volcanic rock that contains iron...
...eh, how much geological detail do you need? XD