Knit and purl blocks to create folding fabric/ “pleats”

Knit and purl combinations  may be executed in hand or machine knitting. Knit charts are generally planned and illustrated based on the fact that the same side of the fabric is always facing the knitter. Hand knitters have to accommodate for the fact that the the work is turned over (unless knit tubular) with every row worked, so plans would need to reverse knit for purl and vice versa if needed. For more ribbed, pleated/ folding fabrics please see 

The easiest way to produce this particular fabric on Brother machines would be to let your garter carriage do the walking and working. For those of us that do not have that option there are transfer carriages, (I honestly have only used mine once, decades ago, will have to dig it out of moth balls) and transferring needles by hand. Pairs of identical stitch transfer tools  may be used to move stitches from one bed to the other. If the goal is to produce a knit with tension as tight as possible, the latter can be problematic and result in dropped stitches, so testing the yarn and the mode of transfer should be part of swatch trials prior to committing to larger knit pieces.  I found moving stitches between beds one at a time for me was preferable and more reliable

The chart for the initial concept: The number of needles used for “pleats” is constant (7); 3 stitches move up (or down) in turn, indicated by arrows. After the first 3 are transferred, 3 more are now moved adjacent to the now remaining 4 stitches from the opposite bed in order to maintain the total of 7 on each bed, excluding any borders, in which stitch placement remains fixed.

cast on for every other needle ribafter completing cast on rows, set up for pattern by transferring between beds*knit 6 rows, transfer between beds  knit 6 rows, transfer again restoring original selections**repeat * to **; transfer to main bed, bind off. Swatch on KM prior to binding off 

If the goal is to retain the texture, it is best to knit using a yarn with “memory” such as wool, which may be steamed or blocked lightly while retaining the fabric’s quality. A rayon or cotton would flatten permanently if pressed. The photo shows both sides of my swatch, beginning on left with it slightly stretched with pins, relaxed in center, and with a bit of vertical “tug” 
The fabric changes a bit when some stitches remain fixed on alternating beds, and the same sort of approach is used. My initial intent had been to transfer every 4 rows, but I actually did so after every 6 rows knit. Colors in chart on right:Its numbers indicate the working needles on each of the 2 beds. The first 3 needles on either side are never transferred. Groups on either bed after transfers remain constant at 6 with the exception of the borders . The starting set upand the alternating one, repeated in turn throughout the knit. Note border stitch selection, constants in between still on the machine 
and my small test swatch. The fold on each side and the swing in the pattern appear crisper and better defined to me
What of horizontal folds? Transferring every stitch to and from the main bed manually is more than I am willing to deal with in addition to transfers for those blocks. I am also interested in the effect produced with use of thicker yarn. This repeat is presently on my hand knitting needles, is suitable for electronics or punchcard machines. A single unit is 5 by 16 rows, the punchcard repeat is 24 X 16 X 3; 32 rows is a tad shy of enough rows for the punchcard to roll and advance properly, 36 rows in height is the recommended minimum. Knitting as tight as possible makes for a stiffer, crisper fabric. I decide there were things about this repeat I did not like however, including the change in pattern at the folds 

The new repeat , with only 2 rows worked rather than 4 between block pattern reversal, the repeat is now 12 rows rather than 16 in height

The hand knit swatch, using 4 ply yarn on #5 HK needles. The arrows mark area where 4 rows were knit between knit and purl blocks rather than 2, creating an added ridge, and a straighter line than the row pairs

an attempt at a side view

Getting rid of those blocks altogether: a generously shared free pattern on ravelry , and a link to the author’s blog