Structure of The Sequence
The 64 hexagrams are grouped into 32 pairs. For 28 of the pairs, the second hexagram is created by turning the first upside down (i.e. 180° rotation). The exception to this rule is for the 8 symmetrical hexagrams that are the same after rotation (1 & 2, 27 & 28, 29 & 30, 61 & 62). Partners for these are given by inverting each line: solid becomes broken and broken becomes solid. These are indicated with icons in the table below.
Given the mathematical constraints of these simple rules, the number of lines that change within pair partners will always be even (either 2, 4, or 6). Whereas the number of lines that change between pairs depends on how the pairs are arranged, and the King Wen Sequence has notable characteristics in this regard. Of the 64 transitions, exactly 48 of them are even changes (32 within-pairs plus 16 between-pairs) and 16 are odd changes (all between-pairs). This is a precise 3 to 1 ratio of even to odd transitions. Of the odd transitions, 14 are changes of three lines and 2 are changes of one line. Changes of five are absent.
| 1 ↕ 2 | 3 ~ 4 | 5 ~ 6 | 7 ~ 8 | 9 ~ 10 | 11 ~ 12 | 13 ~ 14 | 15 ~ 16 |
| 17 ~ 18 | 19 ~ 20 | 21 ~ 22 | 23 ~ 24 | 25 ~ 26 | 27 ↕ 28 | 29 ↕ 30 | 31 ~ 32 |
| 33 ~ 34 | 35 ~ 36 | 37 ~ 38 | 39 ~ 40 | 41 ~ 42 | 43 ~ 44 | 45 ~ 46 | 47 ~ 48 |
| 49 ~ 50 | 51 ~ 52 | 53 ~ 54 | 55 ~ 56 | 57 ~ 58 | 59 ~ 60 | 61 ↕ 62 | 63 ~ 64 |
Read more about this topic: King Wen Sequence
Famous quotes containing the words structure of, structure and/or sequence:
“I really do inhabit a system in which words are capable of shaking the entire structure of government, where words can prove mightier than ten military divisions.”
—Václav Havel (b. 1936)
“A committee is organic rather than mechanical in its nature: it is not a structure but a plant. It takes root and grows, it flowers, wilts, and dies, scattering the seed from which other committees will bloom in their turn.”
—C. Northcote Parkinson (1909–1993)
“Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with sequence and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange form—it may be called fleeting or eternal—is in neither case the stuff that life is made of.”
—Walter Benjamin (1892–1940)