Not even sure what the proper name is, but here is how I make them. Please let me know if you have questions in the comments and I will answer them there.
Materials:
- 4 yarn colors. I almost always use Cascade 220, mainly because I love the way it knits and crochets up, its affordable wool yarn, and has a beautifull array of colors to choose from. Use what you prefer, adjusting your gauge and hook size as necessary.
- Size G/4 Crochet hook- I use Clover Soft Touch Crochet hook. I like these fairly tight, and I recently switched from a H/5 hook because I wanted them small and dense. You do what works for you.
Abbreviations:
bet- Between
ch- Chain
dc- Double Crochet
sl st- Slip Stitch
rnd- Round
To Make:
1. Using the color you chose for the very center, put the yarn on the hook using a slip knot. Ch 5-
Sl st into first ch to form a circle-
Rnd 1- Ch 3 (counts as 1st dc), 11 dc into the circle. Here is how mine looks half way round-
Sl st to join (12)-
Rnd 2- Change to 2nd color. Ch 3 (as previously, counts as first dc) into space between previous row's dc, then dc into same space. Like this-
Continue doing 2 dc in each space, and sl st to join into a circle (24).
Rnd 3: Change to 3rd color. Ch 3 into one of the spaces between the dc sets in previous round-
Make 2 dc into the same space, then proceed to make 3 dc in each space between the previous rounds dc sets. Sl st to join into a circle. (36) This is what yours should look like-
Rnd 4: Change to color 4 (you may want this to be the same color in all your squares).
Join with ch 3 in between one of the spaces between the 3 dc sets in the previous row. 2 dc into same space, then ch 1, like this-
Dc 3 times into next space. Then ch 3 (you're making your first corner)-
*Dc 3 times into next space, ch 1. Dc 3 times into next space, ch 1. Dc 3 times into next space, ch 3.*
Repeat between * * twice more.
Dc 3 times into next space, ch 1 and sl st to join. Your finished granny square (with a circle center) should look like this-
These come out a bit rounded, but once the grannies are joined they will be square, like this-
To join your grannies together, I point you to this video (not the greatest video, but it helped me learn and at least his nails weren't long and bright like some of the others). I use the single crochet method he describes, and the "ridge" created is on the back of my work.
To make a pillow like the one picture at the top, I needed 25 of these granny squares with circle centers for the front, and 25 for the back. 50 may sound like a lot. By comparison, for Truly's pillow, I used a larger hook, but same yarn, and needed 16 squares for the front, and 16 for the back. Once you start making these, you will see how fast they go.

