Elfweave is awesome. You cannot resist it. You must make Eeeeeeeelfweeeeeeeeave... *spooky fingers* Elfsheet is a weave by Nadrendion, so thank him for making such a kick-butt weave.
You can make Elfweave with an aspect ratio down to about 4.2. 16swg 1/4", 18swg 3/16" and 20awg 1/8" rings make very nice Elfweave. Bumping up the inner diameter will make it easier to weave.
Metric sizes - approximately 0.8mm wire/3mm ID; 1.2mm wire/4.8mm ID; 1.5mm wire/6.4mm ID.
Silver rings are old rings, gold rings are new rings being added in the current step and bronze rings are rings that the gold rings pass through.
Step 1a: Notice the blue sections below. These are eyes that the 4 rings make. These eyes are what the rings you'll be adding are going to go through.
Step 2: Pass a ring through the eyes highlighted above, making sure that the left set of rings keeps its inverted-V orientation and the right pair of rings keeps its proper-V orientation. Note that the rest of the 2-1 chain hasn't had anything done to it; it's just scrunched up tighter together.
Step 3: Flip the whole thing over. The rings that had the proper-V orientation in the last step should now be forming an inverted V. The next pair of rings should now make a proper V. Pass a ring through these sets of rings in the same manner as in Step 2.
Step 4: Flip it over again, and add a ring through the eyes. Remember that the first set of rings you pass through (the left-most rings in these diagrams) should have an inverted V orientation and the second pair of rings (the right-most rings) should have a proper V orientation.
Step 5: Repeat Steps 3 & 4 until you run out of 2-1 chain. If you find that the patch is not as long as you wanted it to be, you can add additional 2-1 chains to the end of the patch and repeat Steps 3 & 4 again.