Understanding Hexagram Orderings

King Wen (Traditional Sequence)

The King Wen sequence is the received ordering of the 64 hexagrams, standard for roughly three thousand years. It is the arrangement found in virtually all I Ching translations, commentaries, and traditional practice.

The sequence divides into two halves: the Upper Canon (hexagrams 1 through 30), which addresses cosmic and natural forces, and the Lower Canon (hexagrams 31 through 64), which addresses human and social dynamics. Within this structure, every two consecutive hexagrams form a complementary pair — 32 pairs in total. Each pair presents two sides of the same dynamic, typically as structural inversions of one another.

The King Wen ordering is not random or arbitrary. It traces a coherent progression from the primal forces of the Creative and the Receptive through cycles of growth, obstruction, renewal, and transformation, closing with the mirror pair of After Completion and Before Completion — equilibrium achieved and already drifting, equilibrium approached and not yet secured.

For a detailed breakdown of the King Wen structure including six thematic arcs and all 32 complementary pairs, see the Our Approach page.

When to explore this ordering: This is the default. It connects to the vast majority of I Ching literature and commentary, and it is the ordering that preserves the narrative and structural logic of the received text.

Mawangdui (Silk Manuscript Sequence)

In 1973, archaeologists excavated a tomb at Mawangdui (馬王堆) in Changsha, Hunan province, that had been sealed in 168 BCE. Among the finds was a silk manuscript containing all 64 hexagrams in an arrangement completely different from the King Wen sequence. This is the oldest surviving physical arrangement of all 64 hexagrams.

The Mawangdui ordering is organized by upper trigram in family order: Qián, Gèn, Kǎn, Zhèn, Kūn, Duì, Lí, Xùn. Within each group of eight, the lower trigram cycles through the same family order, with the pure doubled trigram (for example, ☰ over ☰) placed first. The result is eight clean octets — the grouping principle is trigram composition, not narrative or moral pairing.

Important note: The text displayed on this site when using the Mawangdui ordering is from the received Zhouyi, not the Mawangdui variant readings. The Mawangdui manuscript contains its own textual variants — different hexagram names and some differing line texts — but this site applies only the ordering, not those textual differences.

What it reveals: Physical manuscript evidence that the ancients organized hexagrams by structural composition — which trigrams are present — not just by narrative sequence. The eight-trigram grouping makes it immediately visible which hexagrams share an upper trigram.

When to explore this ordering: When you want to see hexagrams grouped by their upper trigram and understand how trigram families relate to one another.

Eight Palaces (八宮 bāgōng) — Jing Fang System

The Eight Palaces system is attributed to Jing Fang (京房), a Han dynasty scholar and diviner (77–37 BCE). It is a later structural and divinatory classification system — not the site's primary editorial frame, but a historically important way of organizing the hexagrams that reveals transformation relationships between them.

The system organizes the 64 hexagrams into eight "palaces," each headed by a pure doubled trigram (☰☰, ☳☳, ☵☵, ☶☶, ☷☷, ☴☴, ☲☲, ☱☱). The palaces follow family order: Qián, Zhèn, Kǎn, Gèn, Kūn, Xùn, Lí, Duì.

Within each palace, hexagrams are generated by a mutation algorithm. Starting from the pure doubled trigram, one line is flipped at a time from bottom to top — lines 1, 2, 3, 4, and 5 in succession. After the fifth mutation, line 4 is flipped back, producing the "wandering soul" (遊魂 yóuhún) position. Finally, the entire lower trigram is complemented, producing the "returning soul" (歸魂 guīhún) position. Each palace therefore contains exactly eight hexagrams: one pure, five single-line mutations, one wandering soul, and one returning soul.

What it reveals: The hexagrams as a family tree. Each hexagram belongs to a palace and has a defined structural relationship to its parent trigram. The mutation algorithm shows how one state transforms into another through minimal changes — a single line flipping at a time.

When to explore this ordering: When you want to understand hexagram relationships as transformations — how one hexagram becomes another through single-line changes.

Binary (Fu Xi / Shao Yong Sequence)

This ordering is often attributed to Fu Xi (伏羲), the mythological figure said to have discovered the trigrams, but the systematic binary arrangement was developed by Shao Yong (邵雍) during the Song dynasty in the 11th century CE.

Hexagrams are ordered by their six-line binary value, from 000000 through 111111. The convention used on this site is: 0 = yang (solid line), 1 = yin (broken line), reading from line 1 (bottom) to line 6 (top). This treats each hexagram as a 6-bit number and sorts them numerically.

When the German mathematician Gottfried Wilhelm Leibniz encountered this arrangement in 1703 through correspondence with the Jesuit missionary Joachim Bouvet, he recognized it as equivalent to his own binary number system — one of the earliest encounters between Chinese and European mathematical thought.

Important precision: This site's binary view is a modern structural lens commonly associated with the Fu Xi / Shao Yong binary-style arrangement. It is not itself an ancient canonical received sequence in the way the King Wen ordering is. The binary interpretation is a useful analytical tool, not a historical artifact of equivalent standing.

What it reveals: The pure combinatorial skeleton of the system. All 64 hexagrams are the complete set of 6-bit binary combinations (2⁶ = 64). This view strips away narrative, pairing, and trigram grouping to show the mathematical structure underneath.

When to explore this ordering: When you want to see the hexagrams as a complete combinatorial system, or to understand the mathematical relationship between any two hexagrams.