it's pretty simple, but not as simple as you think.

In India, the agate nodules that are gathered for the production of carnelian are already naturally impregnated with iron--and simple heating makes the material turn red/reddish.

It has been recognized from as early as 2,500 BCE that heat-treating certain stones changes their appearance. It's also reasonable to assume that by logical deduction they figured out that something was in some stones and not in others, that made heat-treating result in color changes. And they set about to determine what you could do to add these colorants to stones. This went on for a very long time, but there is almost no ancient literature that discusses it. A vague reference from the Roman Period is found in Pliny.

The German agate-cutters at Idar-Oberstein (a former Roman outpost, where agate was worked since the Roman Period) brought the coloring of agates to a science. They recognized that certain agates took the treatments better than others (due to "porosity"), and they devised chemical formulas for solutions to permanently make the stones red, yellow, green, blue, and brown. (They also used an organic dye to make a purple or plum agate, but this was a temporary treatment, that is not light-proof.)

The basic and earliest colors, brown and red, were almost certainly known from antiquity.

For brown-to-black, fully dry the stone, and then soak it in a solution of sugar. (Honey or any sugar works.) Then, the stone is burnt to make the color change. If burnt with fire, it caramelizes and turns brown. If burnt with acid, it carbonizes and turns black.

For red, iron nails were disolved in acid (I think it's sulfuric acid), and the stones were soaked in this liquid. Then heating made them turn red. The range of colors is more predictable and rich than often occurs (as at India) from stones that "naturally" have this surplus of iron from the ground.

The success of these treatments depends a lot on the agate. Some material is much more porous than that from other locations. This is also why some decorated stone ("etched") beads are well-made and others are not (the nonporous ones). And, in part, it explains the general trend for these beads and zi beads to be brown or black.

In the 1880s, the Germans discovered that cheap undistinguished agate from Brazil, that was cheap and plentiful, took their coloring processes very well. So, since that time, most of the commercial agate in production for small articles and lots of beads is Brazilian agate, treated by Germans, or by people who learned the art from Germans. In the 180s, Brazil took up the practice. In the '90s, the Chinese began to crank-out tons of stuff. And, of course, now the Chinese make lots of fake zi beads too. There recent carnelian beads--such as you show, are artificially colored (soaked) and heat-treated.

By the way, the German process, as I mentioned earlier, are often misidentified as consisting of "dying the agate." This is absolutely wrong. The process is permanent (whereas dying is not), and the solutions that are made are not dyes (that would be organic compounds). The Germans refer to these products as being "beizen" ("BITE-zen"). The word is difficult to translate precisely, for this context--and unfortunately in 25 years I have never gotten anyone to adopt it. Simply put, it means "steeped in acid." Pickles are beizen; and leather is beizen. "Pickled beads" ? I thought it was funny and evocative..., but no one joined me in the laugh.

Jamey