I was always fascinated with this type of tatting which was invented by Rosemarie Peel. It's what is known as Celtic Tatting. I first saw it in one of her books. This is made simply using two separate motifs and interweaving them. A final row then 'locks' them to form the final motif.
The other later form which involves a long chain which is tied into a knot of some sort is what I personally call Celtic Knot Tatting. A different thing altogether.
Anyway this is a design I did some years ago and it fits into a metal ring (bracelet).