The basic four-strand round kumihimo braid, Maru Yottsu, is a quick and easy way to create a strong braid with simple color patterns.
It’s not a Japanese invention, however, since pretty much every culture in the world figured out how to braid four strands together shortly after the invention of string (or perhaps before, if they had long hair). It can be done on a rope-making stand, a cardboard disk, a marudai, or just with your hands.
Weavers think of it as a way to create tassels and cords, weekend warriors think of it as a way to make tactical climbing rope, and one clever fellow recognized a completely different use, in a comment at the weaving link:
DIY Speaker cable leads. No I’m not kidding.
Weaving four insulated smaller wires in the B-A-A-B pattern results in an Interlaced Dual Twisted-Pair cable. In your example, white would be one twisted-pair, orange is the second twisted-pair. This weave pattern yields a cable of lower electrical resistance, while providing noise rejection that a single thicker wire doesn’t have. Key for high-current delivery and/or to low impedance speakers (exotics, cars). Also great when you only have smaller gauge wire than you want for your application.
To get the Interlaced Dual Twisted-Pair noise cancellation, once the weave is done, you cross connect the twisted pairs. Which means: join one white and one orange at one end, join the same two wires at the other end (continuity meter), then join the remaining white-orange wires together at each end. Run your positive/live through one of the new white-orange pair, and the negative/ground through the other.
Extra credit to the guy who built an oversized marudai out of tires to make a 12-strand climbing rope for Crossfit.
[Update: finally found the page I was looking for in The Ashley Book of Knots, where he describes both the finger-braiding method (#2999, 4-Strand Square Sinnet), and using a table (#3037, #3070) that’s basically identical to a marudai. Amusingly, where marudai braiders are extremely finicky about the smoothly-polished texture of the table’s surface, Ashley drives 1-inch brads into the edges to keep the strands neatly separated.]