King Wen sequence

The King Wen sequence (文王卦序) of the Yi Jing (易經) is a series of sixty-four binary figures (hexagrams), each comprised of 6 lines, either unbroken (yang 陽) or broken (yin 陰).

The King Wen sequence, also known as the classical hexagram sequence, is sometimes considered the second–oldest formal arrangement of the hexagrams, preceded only by the Fu Hsi (伏羲) arrangement, though the Fu Hsi arrangement is most often associated with the Song Dynasty scholar Shao Yong (邵雍). The historical legend is that King Wen of Zhou (周文王) designed this sequence in the 12th century BC while imprisoned by the tyrant King Zhou of Shang; King Wen is said to have died in 1050 BC, by one interpretation of the evidence (Shaughnessy).

Over the centuries there were many attempts to find an underlying mathematical structure to this pattern. The true combinatorial mathematical basis of the classical hexagram sequence was explained for the first time in STEDT Monograph 5: Classical Chinese Combinatorics.

Notable characteristics

The 64 hexagrams are grouped into 32 pairs. The second partner in each pair is created by inverting the first. In 4 of these pairs inversion (i.e. 180° rotation) of either hexagram effects no change (in which case all six lines will change). The number of lines that change between pair partners is always even (either 2, 4, or 6).

In moving from one hexagram to the next a minimum of one line must change. There are no instances in which five lines change. There are nine cases in which all six lines change.

The ratio of even to odd numbers of line changes between the hexagrams is exactly 3:1.

64 hexagrams x the 6 lines of a single hexagram = 384, the same number of days as found in ancient annual lunar calendars (that were based on 13 'months' of lunations).