A lot of the message threads I found referenced a Google Sites page that's no longer there, but the general gist I was able to glean is that fountain pen ink has 4 or 5 ingredients:
-Water - fairly obvious.
-Dye - gives the ink color. Too little and the ink is too light, too much and it's too dark (and may also clog your pen).
-Surfactant - reduces surface tension. Too little and it won't flow well, too much and it'll bleed/feather once on paper.
-Humectant - slows evaporation rate. Too little and it'll dry up on the nib, too much and it'll be annoyingly slow to dry on the page.
-Biocide/preservative (optional) - stop mold. Too little and the ink will go bad, too much and it'll be poisonous.
The other takeaway was that it's pretty easy to make, although a) it's really tough to get consistent colors due to needing to keep all the ingredient amounts constant, and b) there's a risk of messing up pens due to clogging or corrosiveness. As I've got a milligram scale for measuring pure caffeine, keeping ingredients consistent shouldn't be too crazy difficult, and as I've got dozens of $1-$2 pens (I buy Jinhao sharks by the case specifically for trying out inks) I'm not concerned about a couple of them possibly being sacrificed to the altar of science.
(I've put Amazon links at the end of the article if you want to buy any of these.)
Water is water. Use distilled to be on the safe side. It's $0.99 for a gallon at the grocery store.
The surfactants mentioned were dish soap and Kodak Photo-Flo, one of the chemicals used in the process of developing film. Because I like taking the complicated route, I went with Photo-Flo.
Humectant recommendations were vegetable glycerin and propylene glycol. I went with propylene glycol because why not.
Dye is the tricky part. There are a lot of options, but I ended up going with powdered aniline dye because I had prior experience with it from some woodworking a couple years back. So far I've tried Keda Aniline Wood Dye and Jacquard Acid Dye; I also have some Jacquard Procion MX Dye in the mail, as I saw it recommended for being very permanent (at least on cellulose-based paper, which is most of them).
The two biocides I saw recommended were salicylic acid and phenol. Seems like salicylic acid is safer and phenol is more effective. I bought some phenol but haven't even opened the bottle yet because I'm still just figuring out colors and the oldest batch I have is under a week old right now, so not at any real risk of mold. (In terms of safety I'm not overly concerned; the quantities involved are very low and the main risks seem to be around the levels of chronic exposure experienced by people working with phenol in an industrial capacity.)
First, I made 1% and 10% solutions of both propylene glycol (PG) and Photo-Flo (PF). Trying to add either of these undiluted into an ink will be incredibly difficult due to the minuscule amounts you need.
I also made a batch of solvent that's just 10ml of distilled water with 0.1 ml each of the 1% PG and 1% PF solutions, for diluting inks to make them lighter.
For all of the dyes I got, I made a base solution of 1 gram of dye powder and 10ml of water. The only exception is the Keda black dye; it appears much stronger and 1 gram wouldn't come close to completely dissolving in 10ml of water, so I diluted it out to 40ml.
For the Keda dyes, I mixed in 0.1ml each of the 1% PG and 1% PF solutions for each 10ml of ink (so, 0.4ml for the black). I also made a batch of solvent that's just 10ml of distilled water with 0.1 ml each of the 1% PG and 1% PF, for diluting to soften the colors.
For the Jacquard dyes, I didn't include the PF/PG, and instead added that to the final inks I made.
There's no reason not to use these as inks in their unmixed form, but where's the fun in that? I only have a pen using the black ink right now, the rest are just for mixing together. Here's what they all look like (note: the ones that say "glass pen" were written with a glass dip pen instead of a proper fountain pen, which results in more ink being deposited on the page and so a darker shade resulting), as well as the recipes used for each one (although I also wrote it above).
So far I've made 5 different mixes that I've liked enough to load into fountain pens and assign ID numbers for easy future reference. The specific recipes are in the image; I could write them out here but you need to look at the picture anyway to see what color it is so it doesn't seem necessary.
All together now
Here are all 12 inks, in one photo for slightly easier comparison.
Is it worth it?
Complicated question. If you factor in the theoretical value of my time, absolutely not, but that's partly because I'm hilariously overpaid and partly because I spend way too long doing things like this more precisely than is really necessary. If you just look at the ingredients involved, and don't include the nice-to-have-but-not-strictly-required lab tools I list below, and if you accept the not-yet-certain assumption that this ink won't, in fact, destroy my Lamy 2000 (which sure as hell won't see this ink until it's worked properly in a cheap pen for at least a couple months with no issues), then possibly.
Let's calculate a rough per-unit cost.
You can get 25 grams of the Keda black dye for $18 on Amazon.
A liter of distilled water costs $0.25 (well, a gallon costs about a dollar).
Using the formula I did, you'd also need 0.1 milliliters each of Kodak Photo-Flo and propylene glycol. If you're making this in bulk, that amortizes out to nothing. Let's assume you're making a single batch but can buy a tiny bit off some local photo shop or something for a couple bucks. (If you're making a single batch and can't split the cost, it's annoyingly expensive, but let's be optimistic.)
That works out to about $20 per liter, which sounds expensive if you aren't used to fountain pen ink, but the comparably-colored Diamine Gray runs $250 per liter (the comparable Noodler's Lexington Gray is cheaper, at $140 per liter, but in general Noodler's inks are fairly slow-drying (albeit waterproof once dry), so I find them inconvenient to use in most cases).
(In fairness, the other dye colors are more expensive per unit volume than the black, due to the higher concentration required, but the ones I've made end up maxing out at $80 per liter.)
So, cheaper than real ink, but if you want a dark/vibrant color, only by a factor of 2-4. That's certainly something, but not really a great reason to make your own. It makes a lot more sense if you're the sort of person who wants to get really involved in every aspect of your hobbies, or if you're really, REALLY particular about ink colors. Also if you're looking for one of those hobbies that can be self-supporting with a bit of luck, as you may be able to sell ink to fellow pen enthusiasts and possible make enough to cover at least the cost of the ingredients (I definitely wouldn't count on using this to pay the bills, though).
Complete ink journal
This is the entirety of the journal I'm using to keep track of the ink work (minus the two pages already shown above with the index of color IDs and recipes). Gives a bit of an idea the sort of trial and error that goes into figuring out what inks look good.
Links for learning stuff
Reddit thread about DIY ink.
FountainPenNetwork thread about DIY ink.
FountainPenNetwork thread about ink biocides.
If anyone has other good links to info on DIY ink, I'm happy to add it here. Likewise, I'll update this list with other useful ones I encounter.
Links for buying stuff
Disclaimer: the Amazon links are affiliate links, so I get a tiny pittance if you buy stuff through them, but they're all stuff I used in making my own ink and not random things I'm trying to get people to buy. (My integrity absolutely has a price and can be bought, but it costs way more than the $7.30 I've made in the last two years through affiliate links.)
The non-Amazon links are not affiliate links and I get nothing from you using them, apart from the knowledge that I sent business to places that have treated me well in terms of customer service in the past, and that's honestly worth more than the tiny trickle of affiliate earnings.
Keda aniline wood dye - Good starter set, but I might go straight to Jacquard dyes were I doing this again.
Jacquard crimson and Jacquard brilliant blue - Cheaper to order it from Blick Art Supplies, but I'm lazy.
Photo-Flo - you might be able to get this locally if there's a good photography store in town, or, as some places have mentioned, you can just use detergent instead. However, if you want to go with this stuff, here's where I got it. If you know anyone else who's interested in making ink, you can definitely split a bottle; I've used maybe 25 microliters (no, not milliliters) of this stuff so far making 60-70ml of usable ink. If I were less busy I'd offer to sell small bottles of it, but it's really not worth my time. That said, if anyone else wants to, I'm happy to update this with a link to their site.
Propylene Glycol - you can likely get this locally, as well, but I'm lazy. As with the PF, I've used maybe 25 microliters of this stuff so far. Also as with the PF, I'm too busy to sell tiny bottles, but am happy to advertise someone else who does if anyone wants the job.
The following aren't strictly required but have been incredibly useful for making/testing inks. Also, for all of the lab equipment, it's worth looking for either friends with lab access who can get it for you at a discount or free, or places that are selling it cheaply due to it not being in good enough condition for use in a proper lab (e.g., I got the disposable plastic dishes mentioned below for $6 instead of $20 because it was a returned and opened-but-resealed box).
Milligram-precision scale for measuring ingredients - possibly overkill, but overkill is underrated and I already had this lying around. If you don't care about exactly recreating a color down the road, may as well just trust the manufacturer's word for how much dye is in each jar you buy and mix it all with water from the get-go.
Disposable pipettes for rough ink measurement - you can probably just get a couple and clean them out, but to be on the safe side, disposable ones aren't all that expensive and you can always save them and wash them, just less frequently than if you only have a dozen. Could also just use drinking straws.
Syringes with dull needles for precise ink measurement - especially useful for measuring the PF and PG solutions. I usually use the pipettes for ink if I need to measure by the drop (for testing mixes) or the ml (for making full batches), but these are useful for getting .1ml or .05ml of a liquid. You can also get syringes and needles pretty cheaply at CVS or the grocery store (at least, you used to be able to), but they're a) sharp and b) more expensive if you want a large number. Also, the person at the counter will look at you suspiciously even after you explain that they're for filling fountain pens and not shooting up heroin.
Disposable plastic dishes for mixing colors - if you're opposed to disposable products, definitely don't get these, but I find them way easier than having a half-dozen or a dozen tiny dishes to wash out after each time I make inks, and I was able to pick up a returned box for a bit over 1 cent per dish. Cheaper but slightly more labor-intensive alternative is folding tiny dishes out of tin foil.
Plastic bottles for storing samples - these are identical to the ones used by GouletPens.com for ink samples, just with blue lids instead of white. I already had them lying around as I use them to hold painkillers while running; there may be other, better alternatives available, especially if you've gone through a lot of commercial ink and have saved the bottles.
Marking tape for marking samples - you could probably also use masking tape or just write directly on the vials, but I've found this sticks better long-term than other tapes while still being removable. However, it has no adhesion whatsoever to certain types of glass used in small sample vials.
Rack for holding samples - this appears to be the same one sold by GouletPens.com, but for about half the price and with Prime shipping. If you want to support an awesome specialty retailer, buy it from Goulet. If you're like me and already regularly spend far too much money at Goulet and want to save a couple bucks this time, buy it from Amazon.
Jinhao 993 Shark pens for testing inks - $1.50 each for a dozen fairly solid pens. Only downside is that they're a bit inconsistent in terms of ink feeding; that said, it's still cheaper to try out an ink in 3 sharks than pretty much any pen that's better. You can get them cheaper on AliExpress and possibly elsewhere, but this is cheap enough and much faster than waiting for delivery from China.