Short answers, pulled from the story.
Tyrian purple is a reddish-purple natural dye secreted by predatory sea snails in the family Muricidae, particularly Bolinus brandaris, Hexaplex trunculus, and Stramonita haemastoma. The coloured compound is 6,6'-dibromoindigo. It is named for the ancient Phoenician city of Tyre, in what is now Lebanon.
Producing Tyrian purple required enormous quantities of snails and substantial labour. According to scholar David Jacoby, twelve thousand snails of Murex brandaris yield no more than 1.4 grams of pure dye, enough to colour only the trim of a single garment. The 4th century BC historian Theopompus recorded that purple dye fetched its weight in silver at Colophon.
By the 4th century AD, sumptuary laws in Rome restricted Tyrian purple exclusively to the Roman emperor. Senior magistrates had previously worn the toga praetexta, edged in Tyrian purple, while generals celebrating a triumph wore the all-purple toga picta with gold thread edging.
Production of Murex purple for the Byzantine imperial court ended with the sack of Constantinople in 1204 during the Fourth Crusade. Scholar David Jacoby concluded that no subsequent ruler in former Byzantine territories could assemble the financial resources to sustain the industry. The broader tradition of Murex-based dyeing had begun as early as 1200 BC among the Phoenicians.
In 1998, a researcher rediscovered a workable dyeing process through lengthy trial and error, drawing on historical reports from the 15th through 18th centuries and the biotechnology of woad fermentation. By adjusting the percentage of sea salt and adding potash to an alkaline fermenting vat, and consulting the incomplete recipe left by Pliny the Elder, the researcher successfully dyed wool a deep purple colour.
Murex shell accumulations on Crete suggest the Minoans may have produced imperial purple during the Middle Minoan period in the 20th-18th century BC. Crushed Murex shells at Coppa Nevigata in southern Italy indicate production from at least the 18th century BC. The earliest surviving fabric dyed with royal purple was found in 2021 in the Timna Valley in Israel, dated to around 1000 BC.