Thoughts on Trigrams with Moving Lines

(Copyright © 2003 C. J. Lofting)

Just as with hexagrams with moving lines there are 4096 possible expressions, so with trigrams with moving lines there are 64 possible expressions. With hexagrams the expressions are in the form of static dodecagrams, 12 line symbols that are compressed into the changing-line hexagram format. With trigrams the expressions are in the form of static hexagrams, where the hexagrams reflect the harmonics, the parts, reflected in each whole that is a trigram.

With trigrams there are eight related hexagrams per trigram where each hexagram reflects a state of the trigram under conditions of change. Thus to flesh-out the full set of meanings for changing-line hexagrams we have to focus on 4096 dodecagrams and so to do the same form changing-line trigrams we have to focus on 64 hexagrams.

In any context, be it trigrams or hexagrams or other, line change patterns come in pairs such that we have:

Pure yin line changes into a pair of yin lines, one following the other (00).

Pure yang line changes into a pair of yang lines, one following the other (11).

A changing yin line changes into a pair of yin/yang lines, the yang following on from the yin (01).

A changing yang line changes into a pair of yang/yin lines, the yin following on from the yang (10).

Applying these rules to changing-line trigrams we initially have the set of static-line hexagrams applicable to each trigram given in the following table:

Table 1 - Associating the 64 static hexagrams of the I Ching to 8 changing-line trigrams

TRIGRAMS\CHANGES	No Change	Line 1	Line 2	Lines 1 & 2	Line 3	Line 1 & 3	Line 2 & 3	Line 1 & 2 & 3
HEAVEN	01	13	09	37	43	49	05	63
LAKE	34	55	11	36	14	30	26	22
FIRE	61	42	10	25	60	03	58	17
THUNDER	19	24	54	51	41	27	38	21
WIND	33	44	53	57	31	28	39	48
WATER	62	32	15	46	56	50	52	18
MOUNTAIN	20	59	12	06	08	29	45	47
EARTH	02	07	16	40	23	04	35	64

This table is the equivalent of mapping the 4096 possible static-line dodecagrams to the 64 changing-line hexagrams where for each hexagram there are 64 dodecagrams.

We note that the above process has been derived through applying recursion to a PARTICULAR trigram, working from the base-line upwards. Elsewhere we note that we can also derive another ordering reflecting a GENERAL focus through rotating the hexagrams in the above table to give us:

Table 2 - Rotation of hexagrams in Table 1

TRIGRAMS\CHANGES	No Change	Line 1	Line 2	Lines 1 & 2	Line 3	Line 1 & 3	Line 2 & 3	Line 1 & 2 & 3
HEAVEN	01	14	10	38	44	50	06	64
LAKE	33	56	12	35	13	29	25	21
FIRE	62	41	09	26	59	04	57	18
THUNDER	20	23	53	52	42	28	37	22
WIND	34	43	54	58	32	27	40	47
WATER	61	31	16	45	55	49	51	17
MOUNTAIN	19	60	11	05	07	30	46	48
EARTH	02	08	15	39	24	03	36	63