It even incorporates a systemic paradox (making it also iconic of the human condition, if one's thoughts wander that way): The basic increase is 16 per round, which means that a block more than 10 rounds or so will tend to ruffle and not lie flat because double crochet grows at about 12 increases per round to lie flat. This usually does not matter because most granny squares are about 6 rounds or so, and you sew a bunch of them together to make your blanket. If you make a blanket out of one really big square, you may not care that it does not precisely lie flat -- just more blanket to love. Or your gauge may be loose so it will lie flat. Like any iconic thing, granny squares can work a bunch of different ways for different people, and it's all good.
If you work in a tight gauge, the chain-one spaces aren't too big - but those squares come out pretty hard. I wanted a softer drape, but the chain spaces were fairly big, and I wanted a pattern for a motif that isn't so open but still had the solid bits to enclose ends and open bits to work up fast. I also wanted the option of joining blocks in the last round or stitching blocks together later.
What I came up with clearly does not have the simplicity of the iconic granny square: it is a 2-round repeat. I work it as a coil, which means it has the asymmetry that comes with coils. While it seemed really intuitive for me, I realize it does involve a bit of paying attention. Here's what I came up with that I have enjoyed:
Note: For this pattern, each row instruction has a beginning bit, then a repeated bit that starts with a *. When you get to the **, ignore it until you read the instruction that refers to that mark. This is very traditional pattern notation, but some people may not be familiar with it.
|The first 8 rounds or so|
2. Set up row 1: Ch2, sc in the ring. Attach a marker in the ch space just made - remember to move the marker to the new ch2 space in each round to keep track of where each round begins/ends. (Ch2, single crochet (sc) in ring) 6 more times. Ch2. It may feel strange to end a round with 'chain 2', but this is a coil so we are easing into the beginning of the next round of the coil. Trust me. And don't forget to make the ch2.
3. Set up row 2 - the corner points: Continuing in a coil, (sc, ch2, sc) in marked ch2 sp to make a corner point. Move the marker to the ch2 space just made. *Sc2 in the next ch sp for a side.** (Sc, ch2, sc) in the next ch2 sp to make the next corner point. Repeat from * around one time (3 full times in all, then ending at **).
Note: If needed, attach a marker to each ch2 corner point so you will know them when you see them.
4. (Sc, ch2, sc) in the next ch2 corner space (move marker to ch sp just made). *(Ch2, skip 1 sc, sc in next sc) across to next ch2 corner space ending with a sc into the first sc of the corner. ** Ch2, (sc, ch2, sc) into the ch2 corner space. Repeat from * 3 more times then a bit more to get all the way around the block and end at **. Ch2 to finish the round.
|A completed block, in place|
6. Repeat 4 and 5 for the pattern.
7. Finish off at the end of a round with a slip stitch that 'refinishes' the first sc of the increase in the first (marked) corner. By 'refinish' I mean: make a slip stitch to merge the end of the last round into the square, rather than having a jog at the end. Insert the hook back into the first single crochet of the corner, as if you had not done the last bit (yarnover and pull through the 2 loops) to finish that stitch. Then yarnover and pull through the stitch - to re-finish that single crochet - and through the loop on the hook to finish the slip stitch
For this project I ended each block with Row 4, joining to the neighbor square with (slip stitch to matching ch2 space ch1) instead of (ch2).