What's all this then?

I'm not quite sure where to start with this, but a story needs a beginning of some sort. So:
Once upon a time (which is to say January), my mom signed up for an introductory lace knitting class. My mom has been knitting for a long time, in a small way, but has mostly never bothered with anything very advanced. Scarves and hats, that sort of thing. She feels like she has trouble finishing any project that's big, or that takes a long time. She figured that taking a class would give her a way of making sure she finished a larger-scale project. The class meets one day a month for most of the year, and between each session the students are meant to knit a section of a sampler that can be worn as a shawl.
So she started her class, and started knitting the first lace pattern. At some point, she said to me, "I wish the lace looked nice on both sides!" Because, in a sort of general way, knitted lace tends to have a right side and a wrong side. And if you're knitting something like a scarf, the wrong side ends up being visible here and there, depending on how the scarf is wrapped.
I haven't been knitting for as long as my mom has, but I've spent quite a lot of time learning about knitting lace. The question of right- and wrong-side is one I've thought about off and on for several years. I took her lace pattern, and started tinkering with it, to see if I could come up with something reversible. I had a few specific criteria in mind.

1. It should look the same front and back. I didn't want the kind of pattern that is sometimes described as reversible, but only because the back doesn't look completely awful. I wanted it to be identical, if such a thing was possible.
2. It still needs to be lace. There are some nice knit/purl textures that look the same on both sides, but they don't have delicate holes in them to let the light through.
3. It should be smooth. I didn't want the kind of nubbly texture you get with garter-based lace.
4. It should be reasonably pleasant to knit. A few p2tog-tbl are probably acceptable, but I don't want to ask anyone to knit directional double decreases from the purl side.

There followed many weeks of experimentation, intense frustration, and interesting discoveries. I've learned that you can indeed make reversible lace, and that it is very satisfying. I still surprise myself, when I turn over one of my swatches and it looks the same on the other side. The whole thing has opened up a wide field to explore, and it seems like other people might find it interesting as well. So I'm planning to write about how it works, post stitch patterns, and generally make notes about what I'm doing.