I know natural purple itself was difficult to obtain, but why didn’t they just mix red and blue? Were those also rare? Did it just not work?
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A big piece missing here is that Tyrian purple does not look purple in the sense you’re likely thinking of it. It’s actually a deep red that’s difficult to achieve without crushing a lot of snails. The point of Tyrian purple is that it’s a unique color. There is a cheaper alternative (kind of a muddy purple color), but it’s not going to have the deep dark red color that is Tyrian purple and it’s not going to fool anyone.
I think what’s being left out of a lot of the answers you’re getting is that dyes and pigments (i.e. paint) work differently. Dyes form a chemical bond with the substrate. Pigments are particles suspended in a medium that impart a particular color. When you mix paint, what you’re actually doing is combining the particles so that when you see the color, you’re seeing a combination of the particles, but under magnification, you see both pigments side by side. For example, if you mix red and yellow, your eye perceives the color as orange, but under magnification you see yellow and red particles next to each other.
Dye chemistry is actually incredibly complex. The way a dye works in regards to textiles is that it forms a chemical bond with the substrate (the textile). Substances like wine/etc. that I see have been suggested in this thread are staining rather than actually forming a chemical bond with the textile’s molecules. Historic dyes are not necessarily 1) compatible with one another and 2) compatible with the same substrates. Pairing the right dye with the right fiber type is part of the difficulty. Mixing historic dyes is technically possible but is not as straight forward as mixing pigments. Modern synthetic dyes, particularly those made for the home consumer, have been chemically formulated to work a bit more like paints. Historic dyes that come from plants, animals, etc. function very differently and often do not mix well at all.
To further complicate matters, the sources of blue and red dyes are different. Blue dye was actually pretty easy to source in the ancient world (I suspect some posters are mixing dyes with pigments; blue pigments were rare and incredibly expensive prior to the 17th century). Woad, which is a yellow flower, produces a nice blue dye. In the ancient world, it was widely traded and cultivated throughout Europe (it originated in the Caucuses). Red dye is much trickier. A true scarlet was a rare color in textiles. In the ancient world, the Kermes beetle was the most common source. Like the Tyrian snails, it took a lot of beetles to create a suitable red. Scarlet/red clothing was a status marker and scarlet in particular is associated with specific holy days and feasts. Madder, which is another flower, produces a nice maroon-y color. It was easily available and can actually be further processed and made in to a pigment for painting (i.e. red lake).
To get the cheap alternative purple I mentioned, you would mix woad with madder . That creates a muddy purple-ish color. It is not a Tyrian purple and would never be confused as such.
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