The granny square is, without a doubt, one of those crochet "squares" or "medallions" that are completely synonymous with crochet in most people's minds. Vests made of granny squares became popular in the 60's, and you can make nearly anything of pieced together granny squares. In addition, the afghan on the couch in the Roseanne set is made of granny squares. This is a surprisingly simple and fast pattern, and it looks great in one color or stripes of many colors.
Ch 4, join with a sl st to form a ring.

Rnd 1: Ch 3 (counts as 1 dc), 2 dc into ring, ch 2 (for corner), *3 dc into ring, ch 2, rep from * twice. Join with a sl st to top of turn-ch.

Rnd 2: Work {3 dc, ch 2, 3 dc} into a corner space to form a new corner. *Ch 1 (for new sp), work {3 dc, 2 ch, 3 dc} into next corner, repeat from * twice. Join with a sl st to first dc.

Rnd 3: *{3 dc, 2 ch, 3 dc} into corner to form new corner, ch 1 (for new sp), 3 dc into ch-1 sp of previous row (new filet place), ch 1 (for new sp), rep from * 3 times. Join to first dc with a sl st.

Rnd 4: *{3 dc, 2 ch, 3dc} into corner to form new corner, ch 1, 3 dc in ch-1, ch 1, 3 dc in next ch-1 sp. Rep from *. Join to first dc with a sl st.
From there on, the pattern is pretty self explanatory (and a lot more confusing written out than just taken in common sense). Whenever theres a corner, put 3 double crochets, 2 chains, and 3 double crochets in it. Whenever there's a filet place, put 3 double crochets in it. And wherever there's double crochets to skip over, chain 1.

As far as variations go, there's not much to do but chain the number of chains for filet places and corners, change from double crochets to a different size stitch, or change colors in different places. The granny square, like most simple crochet squares, is all about what you make of it, not how you make it. You can piece together little 3 or 4 round granny squares for an afghan, or even make a large 15 round square for a baby's blanket. It's all up to you.

This pattern node uses crochet abbreviations.

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