Double-knit Moebius recipe
If you pick two different colours, be warned! Due to the single-sided nature of the Moebius, most colour patterns will be beastly to adapt to this approach. Experiment with multiple colours at your own risk!
This recipe as written will produce stockinette on both sides; daring double-knitters can work almost any stitch pattern instead.
First, swatch in your double-knit pattern; for stockinette, cast on an even number of stitches and *K1, sl1 wyif*, repeat to end; turn and repeat until bored.
If done properly, this will form a pretty little tube. Check your gauge - mine was 4.5 sts per inch. Decide about what size you want your Moebius to be , knowing full well that the actual size will rest in the hands of the Knitting Gods. My plan was for a close-fitting Moebius, or about 80 stitches.
Casting on for the double-knit Moebius is an acrobatic sport; my method required 5 circular needles, though I'm sure a simpler version could be worked out eventually. I used 4 16" circs, sizes ranging from 2.25 mm - 3.75 mm, plus the needle the rest of the Moebius is to be worked in - in my case, a 32" 3.5 mm. If you're intending a larger Moebius than I did, a 40" would be better suited.
Working with one yarn:
Take your yarn and using a Figure-8 cast on, cast on across two of the shorter circs. Each needle should have the number of stitches you worked out above; in my case, 160 sts total.
Knit the first row for each needle, being sure to use each needle on itself - you'll end up with a mess if you knit the "top" needle with the other end of the "bottom" needle. The stitches on one needle are seated differently; be sure not to twist them.
Cut the yarn and set this pair of needles aside. Repeat with the other two short circs, this time not cutting yarn. This was a total of 320 sts for me; each needle should appear to have a single row of knitting in the center with live stitches on both sides.
Alternate version for two yarns:
Work as for with one yarn, but do not cut yarn on the first cast on. On the second, PURL the stitches off the Figure-8 cast on. This will make the working yarn land on the opposite corner as would have happened if you'd knit the stitches.
Take both pieces (all four circs) and line them up with working yarn(s) at the top right side and wrong sides facing each other. Keeping the working yarn out of the way, slip the first stitch from the front needle to the long circ, then the first stitch from the back needle to the long circ. Keep slipping stitches in this manner, alternating from which needle, until you reach the end of the top needles. You'll have half your stitches on the long needle and a quarter of your stitches on the other two circs still dangling from your work. (There's no reason why you couldn't knit this round instead of just slipping the stitches, but I found it to be too much going on at the same time.)
Now to join for the Moebius. Still with the end of the long needle in your hand, grab what is now the other end of the other two circs, where the working yarn is still waiting. Rotate the other two needles so they're pointing up - this puts a half-twist into your knitting. Keeping in the same pattern and still ignoring the working yarn, slip the stitches as before. When you reach the end, you should have all your stitches on your long circ, which is looped around twice and looks downright strange. This is how it should be. There should be a small gap on both sides from having knit a couple rows before joinging; this can be fixed when hiding yarn tails in post-production. For the first several rounds, the knitting will be extremely awkward; it's the nature of the beastie.
Place a marker at the start of the round. Here the instructions differ again for if you're using one yarn or two.
Working with one yarn:
Rnd 1: Knit the knits/front stitches and slip the purl/back stitches with yarn in front.
Rnd 2: Slip the knits/front stitches with yarn in back and purl the purl/back stitches.
Repeat these two rounds to form double-sided stockinette.
Working with two yarns:
*With both yarns in back, K1 with first yarn. Bring both yarns forward and P1 with second yarn.* Repeat this across the whole round, every round.
Keep knitting in whatever pattern your heart desires until desired length. Bind off. I used an I-cord bind off-
CO 3 sts, K1 (should be a "front" stitch), slip these four sts back to left needle. * K3, p2tog ("back" stitch), sl sts back to left needle. K3, SSK, sl sts back to left needle.* (Be especially careful after the p2tog that you bring the yarn to the back before slipping stitches!) Rep until all sts are bound off; prettify the start/end of round with yarn tail.
Or use your favourite method of binding off. Hide whichever ends you want hidden, and 'tis done!