The King Wen sequence
The pair rule and the search for a formula
Tap a pair to see whether it is formed by reversal (fan) or by complement (dui).
The Fu Xi sequence is counting in binary from 0 to 63. The King Wen one (the order in which the hexagrams appear in the book) follows no known numerical formula. What it does have is a pair rule: the 64 are grouped two by two, and the second of each pair is the reversal (fan 反) of the first. Only in the 4 pairs whose hexagram is a palindrome (where reversing changes nothing) is the complement (dui 对) used.
Hexagram 1 is a palindrome: reversing it leaves it unchanged, so the pair is formed with its line-by-line complement.
Each bar is the binary value of the hexagram at that position. In Fu Xi it is a perfect ramp; in King Wen, noise. Exactly how much noise is measured by the experiment King Wen as a permutation.
Reversal preserves the number of yang lines, and complementation inverts it (yang ↔ 6−yang). That is why within each pair the two bars are equal (reversal) or add up to 6 (complement): the sequence jumps, but never entirely freely.
The King Wen ordering groups the 64 into 32 pairs: 28 by reversal (fan) and 4 by complement (dui). Reversal preserves the number of yang lines; complement inverts it.
verificar_rey_wenThe types of claim and the full bibliography (APA) are in Foundations.