I know purple was very hard to come by in the ancient era. It came from a specific mollusk, and took a lot of them to dye just one garment. But were there ever alternatives used? If so, what is the source or evidence that they did?
A few things. Purpura is not "purple," it described a number of colors produced by two species of shellfish, which Pliny identifies as being purpura (or pelagia) and buccinum--ideally both types were used to produce the final dye. The resulting dyes came in a number of colors, depending on the shellfish used, the exact process of dying, impurities, and undoubtedly environmental conditions--part of the process involved steeping and exposure to heat. The best purple, "Tyrian purple" was called "twice-dyed" because the fabric was colored consecutively first with the pelagiae and then the bucchina. This generally produced not a purple or violet color, but an extremely dark reddish color (hence the frequent poetic use of "purple" to describe the color of blood) that had some kind of special shine as well. Besides this highly-prized color "purple" came in various shades between intense reds to violets and even greenish-blues--the specific use of the word purpura to describe the color English calls "purple" is a convention of later antiquity.
Not all purple was Phoenician, and even among the Phoenician dyes some cities had better dyes than others. Tyrian twice-dyed purple was the best, because of its rich color, but a similar dye was Laconian purple, from Gythium in Laconia. It was not as good, but was apparently comparable. Further, cheap purples were produced by mixing blue and red dyes in different quantities--red madder dye (itself the cheapest kind of red--more expensive reds were produced from the kermes insect) could be dyed over woad to produce an imitation purple. But it probably didn't fool much of anybody, because of the peculiar qualities of real Tyrian purple and the variations in color that the dye exhibited--the defining characteristic of purpura was not so much a precise (usually reddish) color, but its sheen and richness, which was simply unparalleled because of the process. Further, even cheaper sources of poor imitation dyes could be found in certain lichens and bedstraw (a kind of plant, not like...actual straw...from your bed...).
Finally, the expense of purpura in itself was part of the point. Sure, the dye was richer and more pleasing than most other dyes, but as an indicator of rank the color was all the more highly prized. The use of purpura on the toga praetexta, for example, was as much about the social status inherent in the dye as the color itself--strict social mores and legislation restricted the use of the color. That cost was not the only factor in the use of the dye is obvious--under the Severans the production of purpura became a state-controlled enterprise, and in late antiquity only the imperial household and magistrates were allowed to own any garments with the dye at all. The humiliation of being caught with an imitation dye, which were comparatively obvious to the eye, would have largely precluded its use among the social ranks allowed to wear it, and there was increasingly less interest in the dye among the rest of the population
EDIT: So there's a lot of people who seem to be having trouble with the way that the process introduced variations into the dye, and it probably doesn't help that I haven't provided a detailed description of the manufacturing process. The best description is provided by Pliny, who says that pelagiae and buccina were to be caught alive, at a particular point just before spring, otherwise the dye extracted is of inferior quality--this passage has been much-discussed for some time, since it's not totally clear what Pliny means (he says, for example, that the dyers don't actually know this, which makes no sense). These shellfish (which are, yes, still extant--I believe they're both types of Mediterranean welk) had some kind of gland that had to be removed (either from the still-living animal or immediately after killing it). The resulting liquid would be salted, allowed to steep for three days (a point that Pliny is precise about), then heated for ten days--the apparatus that Pliny describes as used to heat the concoction is problematic, but it appears that it needed to actually be boiling (how it could be boiled in what had to be an open container--since the flesh and impurities that floated to the top were skimmed off--and not boil away after ten days is a mystery to me). The dye was then tested by dipping wool into it, and if the color was unsatisfactory could be boiled longer. It's not clear whether this process applied to both types of purple, since Pliny says that to make twice-dyed purple the cloth had to be dipped in uncooked (whatever that means) pelagiae before being treated with bucchina--the resulting color, Pliny says, was most valuable when it was the shade of congealed blood, and when held up to the light would shine somehow. Even with Pliny's fairly detailed description (which includes, to a certain extent, amounts of the ingredients), this is not a recipe, and it's hard to replicate. Besides that, it's easy to see how the dye might vary. Pliny is quite clear that the quality of the dye depended a great deal on the time of year, and slight variations in the process might have caused enormous differences--the process as described by Pliny had to be simultaneously quite exact (Pliny says that you must not let the liquid steep more than three days before heating it or it starts to lose the best color--surely a certain amount of eyeballing must have occurred) while being pretty open to the judgment of the dyers (hence Pliny's remarks about the dye having to be tested repeatedly). The fact that Tyrian purple was the product of two separate dyes is important as well--even the slightest variations in the composition of the dyes, the degree to which the wool soaked them up, and differences in the ratios (which could not have been exact, given that they're basically dunking the cloth) probably resulted in enormous differences in the color of the fabric--Pliny actually mentions dyes in which the two kinds of purple were mixed together and the fabric dyed only once, so considerable variation must have rested in the precise treatment of the two dyes together. There are other factors here as well. We don't know how exposed to air the concoction was, how long the dye was allowed to soak into the fabric, etc.
As u/XenophonTheAthenian mentioned, they did.
The most common method of creating "false" purple was a two-step dying process, where you would first dye fibers with woad (or indigo, but indigo itself was an expensive and highly prized commodity in Europe until well into the middle ages). Then you'd dye them again with madder.
This practice was actually quite common. There's an interesting study from 2010 that analyzes 18 tunics and dalmatics from Late Antique Egypt, all with purple decoration. The analysis revealed that only one of these eighteen garments was dyed with shellfish-based purple. The other seventeen showed no evidence of brominated indigotin or indirubin components from mollusk purple. Instead, they all showed dye components indicative of a dye from the Rubiacae family--madder. The 2010 study echoes the findings of other studies on Egyptian textile fragments.
So yeah, mollusk-based purple is the dye that Pliny describes in his Naturalis historia. Yes, all those mentions of "Tyrian purple" or "twice-dyed purple" that show up in the Aeneid--and basically everywhere in Latin literature--are referring to mollusk-based purple dye. However, these literary references to mollusk-based purple belie how common "false" purple actually was. In late Antique Egypt, at least, plant-based "purples" were by far the most common. There's also evidence for woad+madder overdeying in Iberia.
But then, the emphasis on mollusk-based purple in the literary tradition speaks volumes about how highly prized it was. Mollusk purple was "royal" purple, and everything else was a cheap pretender.
As a side note, if anyone knows of any Roman/medieval textual sources for plant-based "false" purples, please let me know. None of the articles that I've read have cited any, but I'd be interested to hear if you know of something. u/XenophonTheAthenian, do you have a source for your point that imitation purple dyes would have been "comparatively obvious to the eye"?
Sources (I'll put these into proper citation format when it's not 2:30 am):
Should be noted that this question has been answered 11 months ago by /u/SecondMate https://www.reddit.com/r/AskHistorians/comments/3ve17f/historically_tyrian_purple_dye_was_notoriously/
As a related question, is Titian Red a similar example, where other reds existed but that his was particularly known for some reason? Was this related to the dye itself, to how the painter used it, or to something else?
I can speak at least for the norsemen. Mixing woad (blue) and madder (red) just results in a sort of black. Woad, however does look sort of 'purple' in some ways, so that may be your answer. Woad was one of the more expensive colors, it was time consuming to make a dye of and it was difficult to get a "strong" color from it. So for the norsemen a deeper and more vibrant color would be what a "rich" person would wear and a poor person would wear a very pastel like color as it was much cheaper to come by. So, to answer your question: A norseman with a lot of money might have a very vibrant woad color which would look almost a little purple especially if it was layered with grey dye underneath. So generally they didn't wear purple, in fact I don't think there's any mention of purple in the sagas at all so purple clothes would of been rare. As far as dye/paint goes however there has been found traces of purple on runestones in Köpings kyrka on Öland. So they could make purple color from lichens ( looked very much like magenta ) and they did that, but evidently it was not very effective as all examples of purple paint have faded a lot more than red paint or black paint ( and did not work as purple dye on fabric).