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 work is turned over (unless knitting 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 Pleats: ribbed, folding fabrics , and Origami inspired 2: more pleats and fold using the ribber
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 mothballs) 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 a total of 7 on each bed, excluding any borders, in which stitch placement remains fixed.
cast on for every other needle rib 
after 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 the 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 the 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 up 
and 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 the 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 decided 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 the 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 
an earlier hand knit project in the same stitch family 
Another handknit swatch in worsted weight, perhaps suitable for G carriage 
Its repeat turned 90 degrees clockwise 
Getting rid of those blocks altogether: a generously shared free pattern on Ravelry and a link to the author’s blog
More blocks to try
Zigzags in varied configurations