For millennia, Tyrian purple was the most valuable colour on the planet. Then the recipe to make it was lost. By piecing together ancient clues, could one man bring it back?

When it comes to fabric colors, the answer is no. To match any color that can be seen by the human eye, we require a true cyan, a true magenta, and a true yellow. (It also also extremely valuable, bordering on necessary, to have a true black.) We can synthesize these CMYK colors for use in printing, but not for cloth dying.

This is because a given dye pigment doesn't just have to be the right color; it also has to be compatible with the fiber you want to dye, it has to remain colorfast when laundered and when exposed to UV light, and it has to be compatible with other dye chemicals that may be mixed with it (they must all stain at the same temperature, use the same mordants, etc.).

For example, let's take the Dichlorotriazine (aka Proxion MX) group of dyes, which are the most commonly used dyes in the cotton textile industry because they have superior colorfastness and a large range of compatible pigments. In addition to cotton, they are also used for other natural fibers, such as silk, wool, and linen. Most of the garments you own are probably dyed with Dichlorotriazine pigments.

Table 1 on this page shows all of the Dichlorotriazine pigments in commercial use. Amongst these, here are our best CMYK options:

• C: Turquoise MXG. This is not a true cyan, unfortunately, which means that we cannot perfectly re-create all cyan-containing colors (e.g., blues, greens, greys). It is also the least colorfast of all the commonly used Dichlorotriazine dyes; this means that even if you achieve the exact color you were aiming for, the cloth will stray from that color over time (e.g., green cloth will become more dull and yellowish). If this dye were any other color, it would not pass muster, but the need for some kind of cyan-like dye is so great that the industry is willing to overlook its other shortcomings.
• M: Red MX-5B and red MX-8B. Neither of these are a true magenta, but they at least straddle both sides of true magenta. Red MX-5B is a reddish magenta, and so it is used for mixing warm tones (like orange), while red MX-8B is a blueish magenta and used for mixing cool tones (like purple). Between these two pigments, most magenta-containing colors would be theoretically achievable (if not for the cyan problem), but you would struggle to achieve a true grey.
• Y: Yellow MX-8G. This is an actual true yellow suitable for all color mixing.
• K: Nada. There are no black or grey Dichlorotriazine pigments. If you want to dye cotton black, you have to mix other pigments together to create it, and because we lack for a true magenta or a true cyan, the result will never be a truly neutral black (as becomes apparent if, for example, you make bleach shirts—which reveal that the most commonly used black is actually just a very dark red-brown). It will also never be a really deep, dark, luscious black like we see in, say, polyester fabrics (which are dyed with a completely different family of chemicals).