https://gzw1987-bit.github.io/iching-math/

The King Wen Permutation

A mathematical observation on a 3,000-year-old Chinese text

52 cycle
|
10 cycle
|
2 cycle

The 64 hexagrams of the I Ching have two canonical orderings: the
binary natural order (0-63) and the King Wen sequence (~1000 BCE).
Treating the map between them as a permutation in S64, its cycle
decomposition yields [52, 10, 2] with zero fixed points. 81% of
hexagrams are locked in a single cycle. As far as we can find, this
specific cycle type has not been previously reported.

Verify It Yourself - Read the Paper -

Key Facts

Properties of the King Wen permutation s [?] S64

3
cycles
random expectation: 4.7
0
fixed points
no hexagram stays in place
81.25%
in one cycle
52 of 64
260
order of s
s260 = identity
3.349
mean Hamming distance
random: 3.0
3.2:1
even:odd ratio
parity of cycle positions

Interactive Pages

22 explorations -- everything runs client-side in your browser

The Discovery

 
Verify Permutation
Verify the [52, 10, 2] cycle decomposition yourself
 
Algorithm Animation
Watch the algorithm trace cycles step by step
 
Research Paper (English)
Full interactive paper with reproducible code
 
Research Paper (Chinese)
Zhong Wen Jiao Hu Shi Lun Wen 

The Journey

 
Derivation Journey
13-stage interactive derivation: from Taiji to 384 line texts
 
Retrospective
Project retrospective: how we got here
 
Binary Line Texts
384 line texts in binary representation

Cross-Disciplinary

 
Genome Rearrangement
Genome rearrangement analysis (Hannenhalli-Pevzner framework)
 
Game Theory
Game theory x I Ching mapping
 
Four Minds
Leibniz, von Neumann, Shannon, Petoukhov: independent convergence on
binary x hexagram structures
 
Coupled System
Individual vs. institutional paradox engine
 
Coupled Cycles
Coupled cycle dynamics (early version)
 
Shang Timeline
Shang Dynasty 600-year timeline correlation

Wave Analysis

 
Kondratieff Waves speculative
Kondratieff waves x I Ching phase mapping -- exploratory pattern
comparison, not a causal claim

Binary Explorations

 
Bit Arrangements
Hexagram bit arrangement patterns
 
Bit Forms
Visual forms of binary structures
 
Bit x Morse
Hexagram binary mapped to Morse code
 
Bit x Music
Hexagram binary mapped to musical notation
 
Bit x Voltage
Hexagram binary as voltage signal waveforms
Historical Note: The binary natural order was formalized by Shao Yong
(1011-1077 CE), approximately 2,000 years after King Wen. We do not
claim King Wen "rearranged" the binary order. Our analysis
characterizes the permutation between two independently defined
orderings.

All computation runs in your browser. Zero dependencies. Zero
tracking.

Zhengwen Ge * 2026

GitHub Paper (DOI)