Can you craft purple dye?

To make purple dye, place 1 blue dye and 1 red dye in the 3×3 crafting grid.

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What dye is used for purple?

Tyrian purple
Tyrian purple is a pigment made from the mucus of several species of Murex snail. Production of Tyrian purple for use as a fabric dye began as early as 1200 BCE by the Phoenicians, and was continued by the Greeks and Romans until 1453 CE, with the fall of Constantinople.