Toward a Unified Metaphysical Understanding: Exploring some patterns in the I Ching
 Exploring some patterns in the I Ching
2011-03-01, by John Ringland

There are countless intriguing patterns that can be found within the I Ching. I don't know what they mean, but here we explore some of them... Firstly we map out the correlation between the hexagrams and the binary numbers, and then within this context we explore that patterns formed by the various pairs of hexagrams and groups of pairs.

## Top line is least significant bit for binary interpretation

This is the more common binary arrangement however it goes against the usual bottom-up ordering of lines within the hexagrams. The first line in a hexagram is the bottom line, however here the first '1' digit enters from the top for the binary value 000001 – see hexagram 23 in the top row.

Binary values increase throughout this table from left to right and top to bottom

 Upper → Lower ↓ ☷坤 KūnEarth ☶艮 GènMountain ☵坎 KǎnWater ☴巽 XùnWind ☳震 ZhènThunder ☲離 LíFlame ☱兌 DuìSwamp ☰乾 QiánHeaven ☷坤 KūnEarth 02 ䷁Field 23 ䷖Stripping 08 ䷇Grouping 20 ䷓Viewing 16 ䷏ProvidingFor 35 ䷢Flourishing 45 ䷬Gathering 12 ䷋Obstruction ☶艮 GènMountain 15 ䷎Humbling 52 ䷳Bound 39 ䷦Limping 53 ䷴GradualAdvance 62 ䷽SmallTraverses 56 ䷷Sojourning 31 ䷞Conjoining 33 ䷠Retiring ☵坎 KǎnWater 07 ䷆Legions 04 ䷃Enveloping 29 ䷜GhostRiver 59 ䷺Dispersing 40 ䷧Deliverance 47 ䷮Confining 06 ䷅Dispute ☴巽 XùnWind 46 ䷭Ascending 18 ䷑Corruption 48 ䷯Well 57 ䷸Lady ofFates 32 ䷟Persevering 50 ䷱Vessel 28 ䷛GreatTraverses 44 ䷫Coupling ☳震 ZhènThunder 24 ䷗Returning 27 ䷚Tiger'sMouth 03 ䷂Sprouting 42 ䷩Augmenting 51 ䷲Shake 21 ䷔BitingThrough 17 ䷐Following 25 ䷘Disentangling ☲離 LíFlame 36 ䷣BrightnessHiding 22 ䷕Adorning 63 ䷾AlreadyCrossing 37 ䷤DwellingPeople 55 ䷶Abounding 30 ䷝BrightOmens 49 ䷰Skinning 13 ䷌HarmonizingPeople ☱兌 DuìSwamp 19 ䷒Nearing 41 ䷨Diminishing 60 ䷻Articulating 61 ䷼CentringConnecting 54 ䷵MarryingMaiden 38 ䷥Diverging 58 ䷹OpenExpression 10 ䷉Treading ☰乾 QiánHeaven 11 ䷊Pervading 26 ䷙GreatAccumulates 05 ䷄Attending 09 ䷈SmallAccumulates 34 ䷡GreatInvigorating 14 ䷍GreatBeing 43 ䷪DecidingParting 01 ䷀Force

## Bottom line is least significant bit for binary interpretation

This is the more intuitively correct binary arrangement because it aligns with the ordering of lines from bottom to top within each hexagram. The first line in a hexagram is the bottom line, so it is appropriate that the first '1' digit enters from the bottom for the binary value 000001 – see hexagram 24 in the left column.

Binary values increase throughout this table from top to bottom and left to right

 Upper → Lower ↓ ☷坤 KūnEarth ☳震 ZhènThunder ☵坎 KǎnWater ☱兌 DuìSwamp ☶艮 GènMountain ☲離 LíFlame ☴巽 XùnWind ☰乾 QiánHeaven ☷坤 KūnEarth 02 ䷁Field 16 ䷏ProvidingFor 08 ䷇Grouping 45 ䷬Gathering 23 ䷖Stripping 35 ䷢Flourishing 20 ䷓Viewing 12 ䷋Obstruction ☳震 ZhènThunder 24 ䷗Returning 51 ䷲Shake 03 ䷂Sprouting 17 ䷐Following 27 ䷚Tiger'sMouth 21 ䷔BitingThrough 42 ䷩Augmenting 25 ䷘Disentangling ☵坎 KǎnWater 07 ䷆Legions 40 ䷧Deliverance 29 ䷜GhostRiver 47 ䷮Confining 04 ䷃Enveloping 59 ䷺Dispersing 06 ䷅Dispute ☱兌 DuìSwamp 19 ䷒Nearing 54 ䷵MarryingMaiden 60 ䷻Articulating 58 ䷹OpenExpression 41 ䷨Diminishing 38 ䷥Diverging 61 ䷼CentringConnecting 10 ䷉Treading ☶艮 GènMountain 15 ䷎Humbling 62 ䷽SmallTraverses 39 ䷦Limping 31 ䷞Conjoining 52 ䷳Bound 56 ䷷Sojourning 53 ䷴GradualAdvance 33 ䷠Retiring ☲離 LíFlame 36 ䷣BrightnessHiding 55 ䷶Abounding 63 ䷾AlreadyCrossing 49 ䷰Skinning 22 ䷕Adorning 30 ䷝BrightOmens 37 ䷤DwellingPeople 13 ䷌HarmonizingPeople ☴巽 XùnWind 46 ䷭Ascending 32 ䷟Persevering 48 ䷯Well 28 ䷛GreatTraverses 18 ䷑Corruption 50 ䷱Vessel 57 ䷸Lady ofFates 44 ䷫Coupling ☰乾 QiánHeaven 11 ䷊Pervading 34 ䷡GreatInvigorating 05 ䷄Attending 43 ䷪DecidingParting 26 ䷙GreatAccumulates 14 ䷍GreatBeing 09 ䷈SmallAccumulates 01 ䷀Force

### To transform between these two arrangements

Just interchange:

• Mountain with Thunder (rows)

• Wind with Swamp (rows)

• Mountain with Thunder (columns)

• Wind with Swamp (columns)

## Pair based patterns

The hexagrams are grouped into pairs of consecutive odd and even hexagrams, e.g. 01 & 02 are a pair and so on up to 63 & 64. Now lets plot these pairs on the above matrix whilst forming the pairs into groups based on the symmetries within the matrix.

Above we see 4 patterns made of 16 hexagrams, where each pattern is made of 4 sub-patterns each of which is made of 2 pairs.

### Now altogether...

I really don't know what any of this means, for now I'm just looking for patterns - perhaps some insight might arise by finding and contemplating such patterns...

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