King Wen Sequence
Pair Analysis
The 32 paired hexagrams of the King Wen sequence — each pair connected by inversion (反覆 fanfu) or complementation (旁歸 pangui).
Inverse Pairs
反覆Flipping a hexagram upside down produces its partner. This represents seeing the same situation from opposite perspectives — what appears one way from above looks entirely different from below.
28 of 32 pairs
Complement Pairs
旁歸When a hexagram is symmetrical (its inverse is itself), flipping all lines (yin to yang, yang to yin) produces its partner. These pairs are complete structural opposites.
4 pairs: 1/2, 27/28, 29/30, 61/62
Hamming Distance Distribution
The number of line positions that differ between paired hexagrams. Higher distances indicate greater structural divergence within a pair.
All 32 Pairs
Complete opposites — every line inverted
Mirror image — moderate structural change
Mirror image — moderate structural change
Mirror image — differ by a single line shift
Mirror image — differ by a single line shift
Mirror image — maximum structural change
Mirror image — differ by a single line shift
Mirror image — differ by a single line shift
Mirror image — maximum structural change
Mirror image — moderate structural change
Mirror image — differ by a single line shift
Mirror image — differ by a single line shift
Mirror image — moderate structural change
Complete opposites — every line inverted
Complete opposites — every line inverted
Mirror image — differ by a single line shift
Mirror image — moderate structural change
Mirror image — moderate structural change
Mirror image — moderate structural change
Mirror image — moderate structural change
Mirror image — differ by a single line shift
Mirror image — differ by a single line shift
Mirror image — moderate structural change
Mirror image — differ by a single line shift
Mirror image — moderate structural change
Mirror image — moderate structural change
Mirror image — maximum structural change
Mirror image — differ by a single line shift
Mirror image — moderate structural change
Mirror image — differ by a single line shift
Complete opposites — every line inverted
Mirror image — maximum structural change
Sources & Further Reading
- 序卦傳 (Xugua zhuan, “Sequence of Hexagrams Commentary”). One of the Ten Wings (十翼). The classical source explaining the rationale for pairing consecutive hexagrams.
- 雜卦傳 (Zagua zhuan, “Miscellaneous Notes on the Hexagrams”). Another of the Ten Wings, providing terse characterizations of hexagram pairs as complementary opposites.
- Wilhelm, Richard, trans. The I Ching, or Book of Changes. Rendered into English by Cary F. Baynes. 3rd ed., Princeton University Press, 1967. See “Ta Chuan” (Great Treatise) II.2 on the inversion principle.
- 來知德 (Lai Zhide, 1525–1604). 周易集註 (Zhouyi jizhu). Ming dynasty commentary that systematized the inverse/complement pair analysis (反對).
- Kunst, Richard A. The Original “Yijing”: A Text, Phonetic Transcription, Translation, and Indexes, with Sample Glosses. PhD dissertation, University of California, Berkeley, 1985. Pioneering structural analysis of hexagram pair relationships.
- Hamming, Richard W. “Error Detecting and Error Correcting Codes.” Bell System Technical Journal, vol. 29, no. 2, 1950, pp. 147–160. The original definition of Hamming distance applied here to hexagram binary representations.
- Chan, Augustin. King Wen Sequence as Learning Optimization. Zenodo, 2025. [PDF]