Picture and pattern taken from http://knitting.about.com/od/stitchglossary/g/quaker_rib.htm .
There are many different variations of what is called the Quaker rib, which may be worked on any number of stitches. The simplest involve three or four rows of stockinette followed by three or four rows of reverse stockinette.
This pattern is slightly more complicated, with one row of purls thrown into a field of knit rows, followed later by a wider stripe of reverse stockinette.
Rows 1, 3, 5 and 6: Knit.
Rows 2 and 4: Purl.
Rows 7, 9 and 11: Knit.
Rows 8 and 10: Purl.
Rows 12 and 14: Knit.
Row 13: Purl
Repeat these 14 rows for pattern.
Picture and pattern taken from http://knitting.about.com/od/stitchglossary/g/quatrefoil-eye.htm .
Works on multiples of 8 stitches.
Row 1 (wrong side) and all other wrong-side rows: Purl.
Row 2: Knit.
Row 6: Knit 1, *knit 2 together, yarn over, knit 1, yarn over, slip, slip, knit, knit 3*. Repeat stitches between stars, last repeat will end knit 2 instead of knit 3.
Row 8: Repeat row 4.
Row 10: Knit.
Row 12: Knit 7, *yarn over, slip, slip, knit, knit 6*. Repeat stitches between stars, end with a knit 1.
Row 14: Knit 5, *knit 2 together, yarn over, knit 1, yarn over, slip, slip, knit, knit 3*. Repeat stitches between stars, end with knit 3.
Row 16: Repeat row 12.
Repeat these 16 rows for pattern.