J.M. Berger has been working on the King Wen Sequence of the hexagrams (that’s the traditional sequence), approaching it from an angle I hadn’t thought of or seen elsewhere. He looks at the line changes necessary to change each hexagram into the next: changing all the lines of hexagram 1 to give 2, 2.1.5 to give 3, and so on. And remarkably enough, several patterns and regularities emerge.
He doesn’t claim to have ‘The Explanation’, simply to have discovered some patterns, which he presents in a coloured table where you can look for more.
I love the way the Sequence yields such a variety of patterns, and in so many different configurations. Berger’s patterns emerge when you arrange the hexagrams (as seems natural enough for a set of 64) in rows of 8. Other patterns emerge, especially in the distribution of trigrams, when you arrange them by decades. I suspect there are more to find, for people who are good with this kind of thing, in the distribution of complementary hexagrams (where every line is changed). We’re just getting started.