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Transmutation circles are a fictional element of the anime series Fullmetal Alchemist. They resemble some of the goetic and mystical diagrams of medieval Europe, but with better artistic execution.
Presumably they are meant to convey a sense of Neoplatonism and paranormal science. Some of them are quite beautiful; the artwork draws on post-medieval alchemy in some cases.
In the context of the show, transmutation circles are required to perform any kind of alchemic transmutation, acting much as a catalyst does in a chemical reaction. Because they are not consumed in the transmutation, they can be used repeatedly, and are often worn on items of clothing or as tattoos so they do not have to be drawn for each new transmutation.
The basic idea of the transmutation circle is the power of the circle. A circle represents the circulation of power. By drawing a construction equation on it, the power is able manifest itself. By knowing the flow of power and its laws, you can cope with many things. One who accepts all of that, understands it, and creates... That is what an alchemist does.
- Izumi Curtis, Fullmetal Alchemist, episode 27.