I Ching Matrices

(Copyright © 2002-2003 C. J. Lofting )

The data presented on this page stems from the analysis of the I Ching as an ontology - a parts list of qualities we use to interpret reality. We use this set of qualities on themselves where, in the context of the I Ching, the WHOLE of the I Ching is used to describe ranges of qualities WITHIN a specific hexagram or set of; e.g. the 'pure' yangness of hexagram 01 is a very general term and we can recruit all of the hexagrams of the I Ching to serve as sources of analogy when describing the different qualitative expressions of yangness in different contexts. This method reflects the nature of these sorts of disciplines where The I Ching describes "all there is'' - the same can be said for the discipline of Mathematics as well as the more 'esoteric' disciplines - all of which are metaphors for the species' brain's method of 'object/relationship' processing.

From the perspective of the human brain, in high precision processes where we differentiate to a point, to a 'pure' form, this differentiation is extreme in that the level of purity achieved is an ideal and something not normally seen in the 'everyday' of the Universe. The brain, through the process of recursion, will encode in each part the whole in that the set of qualities derived from recursion are not only used to describe the text but also the context and as such the expression of text+context. Thus 'pure yang' reflects a text and context that is 'the same' but this is rare and each quality has encoded within it a list of all possible expressions given the set of qualities used to derive 'meaning'; thus for the 64 hexagrams, each hexagram has an ordered list made-up of the 64 hexagrams that serves as analogy for describing the expression of a particular hexagram in a particular context.

This list of possibles, when linked to a context allows us to generate a list of probables where there is no guarantee that a specific relationship will definitely be expressed but more so a strong probability that it will be expressed (as in '99.999%'). The process of recursion will order this list qualitatively, from the 'raw' to the 'refined' forms of expression of the specific hexagram being expressed. This ordering also reflects the DEVELOPMENT path of a hexagram from raw to refined. Thus a fully developed hexagram will show both a development history as well as express itself in any of the forms of that development.

Working from the level of the trigrams, we can order the binary sequence of the trigrams thus, using 0 = yin, and 1 = yang:

000, 001, 010, 011, 100, 101, 110, 111

When we do this we find that applying recursion to each of these eight qualities leads to the following eight sequences (which here form a matrix), each focusing on qualitative differences WITHIN a general quality (the general quality being represented by the first symbol in the sequence). Thus the first element reflects the 'basic' form of a quality and all others reflect degrees of that quality from 'highly represented' to 'minimal/no representation'. For example, the quality represented by 000, earth, is found to be a dominating influence WITHIN the quality represented by 100, thunder, and be totally lacking in the quality represented by 111, heaven, thus these sequences identify the degrees of expression of a quality from 'most dominating' to 'least dominating' ignoring the base line determination. As such, thunder has a yangness IN GENERAL but the most dominating influence is that reflected in earth. Psychologically the difference is in gaining balance THROUGH someone (earth - disciple, advocate) or someTHING (thunder - idea, paradigm):

000, 100, 010, 110, 001, 101, 011, 111

001, 101, 011, 111, 000, 100, 010, 110

010, 110, 000, 100, 011, 111, 001, 101

011, 111, 001, 101, 010, 110, 000, 100

100, 000, 110, 010, 101, 001, 111, 011

101, 001, 111, 011, 100, 000, 110, 010

110, 010, 100, 000, 111, 011, 101, 001

111, 011, 101, 001, 110, 010, 100, 000


This same method is applicable to the hexagrams. As such, a hexagram represents a state vector, the wave equation of quantum mechanics, where prior to linking it with a context we have a list of probabilities, one of which will be expressed in the link. The fact that we can identify these processes in the I Ching, stemming from the methodology of recursion, demonstrates the assertions of the
IDM model of the brain that all of our ontologies are particularisations expressing the properties and methods of the neuron where the probabilities approach used in QM is not a result of 'out there' but more so a consequence of the neurocognitive processes, their methods in processing data, 'in here'.

Thus, analysis of the I Ching, its method in deriving the hexagrams etc, shows us recursion at work, the method of deriving a set of qualities used for description through the act of self-referencing and on this page we reveal four perspectives, two 'pure' and two derived, based on the analysis of how the I Ching creates the qualities it uses to interpret reality. Furthermore, these perspectives are, by association to the underlying unconscious processes of object/relationship identifications, perspectives used by the SPECIES, not just by the I Ching (which is a product of, and so a reflection of, the species mind which in turn has developed from the brain processing sensory data and the reflections the abstraction of these processes in such disciplines as quantum mechanics)

The I Ching perspectives here presented give us insights into the full spectrum of a hexagram, from its most 'raw' to most 'refined' forms of expression, both as a form of magnitude (scalar representation, where the sequence of hexagrams function as a form of thermostat and so we can traverse a sequence in reverse) as well as extensions to include direction (vector representation, where the sequence of hexagrams function as a sequence of vectors and so direction-setting - in other words there is no chance of reversal other than going in a cyclic pattern and so manifesting the repeatable). The duel encoding of these concepts reflects the sharing of the same space of the notions of A and NOT-A, (and so Yang and Yin) notions possibly derived from how our senses deal with paradox.

These I Ching perspectives are here presented in the form of matrices where the matrices are associated with a pair of hexagrams; the reason for the pairing is the SAME matrices apply to each member of the pair but are just read in different directions. (although the more temporally-related sequence has restrictions on this - see below)

The first pair of hexagrams to be outlined, and so set the example for all of the other pairs, is that of the 'pure' hexagrams of pure yangness (hexagram 01) and pure yinness (hexagram 02). Note that the numbers used are the traditional numbers given to hexagrams and as such have no direct association with binary numberings (in the below 'Root Horizontal Binary' order you can re-number the hexagrams, from top-left to bottom-right, 63 to 0 where 111111 = 63 and is hexagram 01, 000000 = 0 and is hexagram 02). If I used binary numbering the patterns would become 'obvious' but since the traditional numbering is so engrained in the discipline I have retained those numbers.

Note on Five-Phase associations.

In the IC Plus Matrices for each hexagram, the binary sequences are ordered in scalar values.. BUT knowing the ROWS so one can derive the properties for each five-phase section without resorting the matrices. The matrices are created as 'mirrors' such that one matrix reflects TWO perspectives. Thus for hexagrams, working from the Root Horizontal Binary (scalars), 01 and 02, reading DOWN, and so from TOP LEFT to BOTTOM RIGHT (hexagram 01) the five-phase order is that of the left column below, reading UP, and so from BOTTOM right to TOP left (hexagram 02) the order is that of the right colum below. Each COLUMN also takes on this format. Thus reading DOWN the column orders are EARTH(1), EARTH(2), WATER(3), WOOD(4), WOOD(5), FIRE(6), METAL(7) , METAL(8). Reading UP the column orders are reversed: EARTH(8), EARTH(7), WATER(6), WOOD(5), WOOD(4), FIRE(3), METAL(2) , METAL(1) :

Earth - Filtration

01 43 14 34 09 05 26 11

Metal - Competitive Exchange
Mountain - Filtration

10 58 38 54 61 60 41 19

Metal - Cooperative Exchange
Water - Consumption

13 49 30 55 37 63 22 36

Fire - Distribution
Wood - Production (refined)

25 17 21 51 42 03 27 24

Wood - Production (raw)
Wood - Production (raw)

44 28 50 32 57 48 18 46

Wood - Production (refined)
Fire - Distribution

06 47 64 40 59 29 04 07

Water - Consumption
Metal - Cooperative Exchange

33 31 56 62 53 39 52 15

Mountain - Filtration
Metal - Competitive Exchange

12 45 35 16 20 08 23 02

Earth - Filtration

Pair 01/02

Root Vertical Binary (vectors)

Quality Matrix (0 to 63) (tensors)

Root Horizontal Binary (scalars)

Balance Matrix (exaggerate/balance)

01 44 13 33 10 06 25 12

43 28 49 31 58 47 17 45

01 43 14 34 09 05 26 11

01 43 14 34 09 05 26 11

09 57 37 53 61 59 42 20

 

10 58 38 54 61 60 41 19

10 58 38 54 61 60 41 19

14 50 30 56 38 64 21 35

 

13 49 30 55 37 63 22 36

13 49 30 55 37 63 22 36

26 18 22 52 41 04 27 23

 

25 17 21 51 42 03 27 24

25 17 21 51 42 03 27 24

43 28 49 31 58 47 17 45

 

44 28 50 32 57 48 18 46

46 18 48 57 32 50 28 44

05 48 63 39 60 29 03 08

 

06 47 64 40 59 29 04 07

07 04 29 59 40 64 47 06

34 32 55 62 54 40 51 16

 

33 31 56 62 53 39 52 15

15 52 39 53 62 56 31 33

11 46 36 15 19 07 24 02

26 18 22 52 41 04 27 23

12 45 35 16 20 08 23 02

02 23 08 20 16 35 45 12

In the above example, The initial ORDER of the hexagrams, as determined by the traditional development of hexagrams line-by-line, bottom-up, is given in the above table under the column heading of "Root Horizontal Binary"; this order is the result of applying recursion to the yin/yang dichotomy and we can stretch this matrix out into a sequence of 64 hexagrams (e.g. see the bottom row of the diagram at http://pages.prodigy.net/lofting/DIAG1.gif ) , stretching from bottom-right pure yin (02) to top-left pure yang (01). Qualitatively this is stretching from 000000 to 111111 where 0/1 represent yin/yang lines in the hexagrams and as such can be given numeric values for 0 (000000) to 63 (111111).

The order in the "Root Horizontal Binary" (RHB) format is reversible in that the order starts bottom row, right and move up the format to top row, left, thus we start with hexagram 02 and work up to hexagram 01. We can read the sequence in reverse to derive a sequence starting in hexagram 01 OR we can rotate the whole matrix 180 degrees to position 01 in the bottom, right, start position. The derivation process in RHB we can call 'first order recursion' where we are deriving from the realm of the general, and so generic 'yin/yang'-ness a set of differences in expression of this 'yin/yang'-ness at the level of SCALARS - which means the hexagrams reflect magnitudes and no more.

Once we have derived the RHB we find that there is another binary sequence present in the form of focusing on a path through all of the possible line changes within a particular hexagram. This sequence (or resulting matrix when we fold the sequence into rows and columns of 8) is shown above as the "Root Vertical Binary" (RVB) (column 1 in the table). This derivation process we can call 'second order recursion' where we are zooming-in to a particular hexagram. This process will ensure the development of a VECTOR where we see a path 'up' the hexagram that reflects qualitative differences in expressions. In the 'traditional' I Ching this RHB lists all of the hexagrams that result from changing lines in a hexagram but there is more to this that what we find in the traditional commentaries etc on the I Ching and line changes.

The RVB has properties unique to the sequence as we shall see and the RVB shown above is also rotatable in that the given format starts bottom, right, and moves to top, left, reflecting the changing lines path through hexagram 02. Rotating the matrix gives us the changing lines path through hexagram 01 (see the sample line change listing with text for hexagram 01 - http://pages.prodigy.net/lofting/lofting/h01lnx.html) This RVB ordering reflects the degree of influence of the qualities represented by the initial hexagram (in red) in all of the others moving from 'most dominating' to 'least dominating' and as such the process of something turning into its opposite - e.g. 01 into 02, 02 into 01, pure yin into yang, pure yang into yin.

What is immediately noticeable between these two binary sequences is that the RVB is in fact the RHB, the sequence derived through the 'traditional' method of recursion, rotated 180 degrees; thus the order derived from applying recursion to the yin/yang dichotomy, and 'building' hexagrams bottom-up using that method, has both a general format, as in the result of the recursion, as well as a particular format in that the order turned upside down lists the changing line patterns through the particular hexagrams traditionally numbered as hexagrams 01 and 02.

In the I Ching Plus work we have identified a number of patterns within the I Ching, two of which we introduce here in the form of the other two columns in the above table; discussion on the more temporal properties of the RVB, especially in the above format for hexagram 01 (and 02) can be found elsewhere.

The Quality Matrix (The possibles/probabilities)

This matrix is derived here (and derived elsewhere by different means but same result) by swapping the top four rows of the RVB with the bottom four; this reflects a property of recursion I call "Variations on a Theme". Surprisingly, the resulting matrix is an ordering of all of 16 hexagrams of the I Ching such that they can be used as a source of analogy in describing the quality of the line position combinations that are associated with a particular hexagram; in the above table the particular hexagram is hexagram 02 (and when rotated, describes hexagram 01). Thus the sequence moves from no changing lines in 02 through to all changing lines in 02 - a total of 16 possible states that are qualitative differences in the general expression of pure 'yin' that is associated with hexagram 02. The qualitative differences are from the 'lowest' state - here mapped by analogy to the lowest quality expressed by hexagram 23 - housekeeping - [bottom row, right] to the highest possible state reflecting the integration of static and dynamic qualities as expressed by hexagram 43 [top row, left] in its 'highest' qualitative form of 'spreading the word' - the 'true' task of the disciple/advocate types reflected in general in hexagram 02. Overall the qualitative emphasis moves from under-exaggeration of a quality to the over-exaggeration of a quality and as such a listing of possible expressions of a hexagram given a 'push' at some point, and so reflecting the nature of a tensor, a self-contained 'system' that will respond to a force by re-configuring itself to express itself and ensure maintaining of balance.

If we rotate the above Quality Matrix, or just read the matrix top-left to bottom-right, we get the Quality Matrix for hexagram 01. Here hexagram 43 is now the 'bottom' hexagram, used as analogy to describe the 'rawest' expression of hexagram 01 and here we use the 'rawest' expression of 43 as analogy where the emphasis is on being 'pushy'; thus hexagram 01 has at least a raw sense of 'pushiness. Its peak sense is now expressed by 23, but now 23 expresses an over exaggeration of 'housekeeping' (which is an under exaggeration of 23) where the focus is on maintaining the 'true faith' - in the secular realm this is maintaining one's skills since people associated with hexagram 01 are competitive individuals, highly skilled as troubleshooters, negotiators etc.

When reading the matrix bottom-right to top-left, the underlined hexagram at the bottom row, right, position reflects the base general qualitative nature of a hexagram with no reference to specific line positions. The next hexagram, also underlined, in the sequence (read right to left) maps to the qualities of line position 1 (regardless of its yin/yang nature - we are dealing with the line position, not its content). For hexagram 02 that is hexagram 27, reflecting the 'need' to be filled, too little yang. For the hexagram 01 order, determined by rotating the matrix 180 degrees or read it top-left to bottom-right, the under-exaggeration of hexagram 43 emphasises its 'general' nature of 'pushiness and then we move to line position 1 whose qualities are best described by analogy to hexagram 28, reflecting the concept of 'excess', of too much 'yang'. The next hexagram is linked to line position 2, the next to line positions 1 + 2, and then line position 3, 1+3, 2+3, 1+2+3, 4, and so on reflecting moving in a binary ordering 'up' a hexagram from its 'raw' expression to its most refined expression.

The Balance Matrix

The Balance Matrix has been extracted from the RHB by simply reordering the hexagrams in each of the bottom four rows (you could do it to the top four if you liked - this reflects the reversibility within the RHB sequence).

The re-ordering of the hexagrams to give the Balance Matrix gives us a development 'path' where, given the above format, the RIGHT side (and so right column of the matrix) contains hexagrams that semantically reflect states of balance/neutralisation when compared to the expressions of the hexagrams on the LEFT side where these hexagrams reflect exaggerations of the balance set, thus hexagram 01 is an exaggeration of the basic sense of harmony present in hexagram 11. This exaggeration is in the form of an idealist focus on 'purity' and 'perfection' that is reflected in the high energy exertions of hexagram 01.

Thus in the Balance Matrix we find a 'pathway' of energy expressions where, for example, the hexagram sequence of the top row (01 43 14 34 09 05 26 11), read right-to-left, reflects increasing exaggerations of the 'balanced' state described by hexagram 11 such that 26 is a 'slight' exaggeration, 05 is a further exaggeration and so on upto hexagram 01. What is also noteworthy is that the first four hexagrams moving right-to-left (and so from 11 to 09) have a more 'reactive' quality when compared to the other four hexagrams (and so from 34 to 01) that introduce a more 'proactive' emphasis in expression.

Also note that WITHIN the sequence, besides the sequential perspective of energy changes, there is the reflective "exaggerate/balance" perspective such that in row one just as 01 is interpreted as an exaggeration of 11 so 43 is of 26, 14 of 05, 34 of 09.

There are many other patterns derivable from these basic sequences and they are discussed elsewhere (or on the ichingplus list at http://www.yahoogroups.com/group/ichingplus )

Given the above patterns for the sequence from hexagram 02 to hexagram 01, reflecting an ordered set of QUALITIES expressed in binary numbers from 000000 to 111111, we come to the discovery that the above four matrices, derived for hexagrams 01/02, (and in fact the RHB is often treated as the 'traditional binary sequence' of the I Ching) are in fact contained in ALL hexagrams such that EACH hexagram has unique expressions of the above matrices - each hexagram has its own format of sequences and balance/quality matrices and as such the same patterns identified above are reflected in these 'variations'.

The Tables of Matrices

What follows are tables containing the matrices for each PAIR of hexagrams that are structurally opposite in form giving us another 31 tables (and so 62 hexagrams) where the rotatable elements allow us to cover every hexagram in the I Ching.

In these tables I have here focused on the Quality Matrix where I have made hyperlinks to hexagrams of interest. For example, in the below table for pair 43/23, the quality matrix for 43 is read top-right to bottom-left, and the quality matrix for 23 is read bottom-left to top-right. In the reading the first hexagram reflects analogy for describing the GENERAL under-exaggerated format of the hexagram in question (example below, 01 in under exaggerated form serves by analogy to describe the GENERAL nature of 43). The second hexagram reflects analogy for the first line position WITHIN a hexagram and all following hexagrams serve as analogies to describe the qualitative expressions of different line position configurations through the hexagram.

Five rows from the beginning of the matrix we find a pair of highlighted hexagrams, e.g. for hex 43 we find the pair 43 28. The 43 reflects the 'pure' expression of 43, its peak expressing as a static form. The 28 serves as analogy to describe when we move past the static and into the realms of the dynamic in that the LEAST 43 can do is described by 28 (focus is on 'excess', on 'going beyond' - reflected in the doing of 43 in the form of 'spreading the word'). The MOST 43 can do is described by the LAST hexagram in the reading, for hexagram 43, where we read top-left to bottom-right, this is described by analogy to an over exaggerated hexagram 02; manifesting the extremes of devotion involved in 'spreading the word'.

For hexagram 23 we read bottom-right to top-left such that five rows UP from the bottom-right we find the highlighted pair of 27 23. The 23 is the FIRST hexagram in the pair (since we are reading bottom-to-top) and is the 'pure' expression of 23 whereas the 27 is the first step 'past' 23, where we move into the dynamic realm ultimately taking us to the over-exaggerated properties of hexagram 01, the last hexagram in the sequence, being the analogy used to describe the 'peak' performance of 23.

Pair 43/23

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

43 28 49 31 58 47 17 45

01 44 13 33 10 06 25 12

44 28 50 32 57 48 18 46

44 28 50 32 57 48 18 46

05 48 63 39 60 29 03 08

 

06 47 64 40 59 29 04 07

06 47 64 40 59 29 04 07

34 32 55 62 54 40 51 16

 

33 31 56 62 53 41 52 15

33 31 56 62 53 41 52 15

11 46 36 15 19 07 24 02

 

12 45 35 16 20 08 23 02

12 45 35 16 20 08 23 02

01 44 13 33 10 06 25 12

 

01 43 14 32 09 05 26 11

11 26 05 09 32 14 43 01

09 57 37 53 61 59 42 20

 

10 58 38 54 61 60 41 19

19 41 60 61 54 38 58 10

14 50 30 56 38 64 21 35

 

13 49 30 55 37 63 22 36

36 22 63 37 55 30 49 13

26 18 22 52 41 04 27 23

11 46 36 15 19 07 24 02

25 17 21 51 42 03 27 24

24 27 03 42 51 21 17 25

Pair 14/08

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

14 50 30 56 38 64 21 35

34 32 55 62 54 40 51 16

13 49 30 55 37 63 22 36

13 49 30 55 37 63 22 36

26 18 22 52 41 04 27 23

 

25 17 21 51 42 03 27 24

25 17 21 51 42 03 27 24

01 44 13 33 10 06 25 12

 

01 43 14 32 09 05 26 11

01 43 14 32 09 05 26 11

09 57 37 53 61 59 42 20

 

10 58 38 54 61 60 41 19

10 58 38 54 61 60 41 19

34 32 55 62 54 40 51 16

 

33 31 56 62 53 41 52 15

15 52 41 53 62 56 31 33

11 46 36 15 19 07 24 02

 

12 45 35 16 20 08 23 02

02 23 08 20 16 35 45 12

43 28 49 31 58 47 17 45

 

44 28 50 32 57 48 18 46

46 18 48 57 32 50 28 44

05 48 63 39 60 29 03 08

09 57 37 53 61 59 42 20

06 47 64 40 59 29 04 07

07 04 29 59 40 64 47 06

Pair 34/20

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

34 32 55 62 54 40 51 16

14 50 30 56 38 64 21 35

33 31 56 62 53 41 52 15

33 31 56 62 53 41 52 15

11 46 36 15 19 07 24 02

 

12 45 35 16 20 08 23 02

12 45 35 16 20 08 23 02

43 28 49 31 58 47 17 45

 

44 28 50 32 57 48 18 46

44 28 50 32 57 48 18 46

05 48 63 39 60 29 03 08

 

06 47 64 40 59 29 04 07

06 47 64 40 59 29 04 07

14 50 30 56 38 64 21 35

 

13 49 30 55 37 63 22 36

36 22 63 37 55 30 49 13

26 18 22 52 41 04 27 23

 

25 17 21 51 42 03 27 24

24 27 03 42 51 21 17 25

01 44 13 33 10 06 25 12

 

01 43 14 32 09 05 26 11

11 26 05 09 32 14 43 01

09 57 37 53 61 59 42 20

05 48 63 39 60 29 03 08

10 58 38 54 61 60 41 19

19 41 60 61 54 38 58 10

Pair 09/16

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

09 57 37 53 61 59 42 20

05 48 63 39 60 29 03 08

10 58 38 54 61 60 41 19

10 58 38 54 61 60 41 19

01 44 13 33 10 06 25 12

 

01 43 14 32 09 05 26 11

01 43 14 32 09 05 26 11

26 18 22 52 41 04 27 23

 

25 17 21 51 42 03 27 24

25 17 21 51 42 03 27 24

14 50 30 56 38 64 21 35

 

13 49 30 55 37 63 22 36

13 49 30 55 37 63 22 36

05 48 63 39 60 29 03 08

 

06 47 64 40 59 29 04 07

07 04 29 59 40 64 47 06

43 28 49 31 58 47 17 45

 

44 28 50 32 57 48 18 46

46 18 48 57 32 50 28 44

11 46 36 15 19 07 24 02

 

12 45 35 16 20 08 23 02

02 23 08 20 16 35 45 12

34 32 55 62 54 40 51 16

14 50 30 56 38 64 21 35

33 31 56 62 53 41 52 15

15 52 41 53 62 56 31 33

Pair 05/35

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

05 48 63 39 60 29 03 08

09 57 37 53 61 59 42 20

06 47 64 40 59 29 04 07

06 47 64 40 59 29 04 07

43 28 49 31 58 47 17 45

 

44 28 50 32 57 48 18 46

44 28 50 32 57 48 18 46

11 46 36 15 19 07 24 02

 

12 45 35 16 20 08 23 02

12 45 35 16 20 08 23 02

34 32 55 62 54 40 51 16

 

33 31 56 62 53 41 52 15

33 31 56 62 53 41 52 15

09 57 37 53 61 59 42 20

 

10 58 38 54 61 60 41 19

19 41 60 61 54 38 58 10

01 44 13 33 10 06 25 12

 

01 43 14 32 09 05 26 11

11 26 05 09 32 14 43 01

26 18 22 52 41 04 27 23

 

25 17 21 51 42 03 27 24

24 27 03 42 51 21 17 25

14 50 30 56 38 64 21 35

34 32 55 62 54 40 51 16

13 49 30 55 37 63 22 36

36 22 63 37 55 30 49 13

Pair 26/45

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

26 18 22 52 41 04 27 23

11 46 36 15 19 07 24 02

25 17 21 51 42 03 27 24

25 17 21 51 42 03 27 24

14 50 30 56 38 64 21 35

 

13 49 30 55 37 63 22 36

13 49 30 55 37 63 22 36

09 57 37 53 61 59 42 20

 

10 58 38 54 61 60 41 19

10 58 38 54 61 60 41 19

01 44 13 33 10 06 25 12

 

01 43 14 32 09 05 26 11

01 43 14 32 09 05 26 11

11 46 36 15 19 07 24 02

 

12 45 35 16 20 08 23 02

02 23 08 20 16 35 45 12

34 32 55 62 54 40 51 16

 

33 31 56 62 53 41 52 15

15 52 41 53 62 56 31 33

05 48 63 39 60 29 03 08

 

06 47 64 40 59 29 04 07

07 04 29 59 40 64 47 06

43 28 49 31 58 47 17 45

01 44 13 33 10 06 25 12

44 28 50 32 57 48 18 46

46 18 48 57 32 50 28 44

Pair 11/12

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

11 46 36 15 19 07 24 02

26 18 22 52 41 04 27 23

12 45 35 16 20 08 23 02

12 45 35 16 20 08 23 02

34 32 55 62 54 40 51 16

 

33 31 56 62 53 41 52 15

33 31 56 62 53 41 52 15

05 48 63 39 60 29 03 08

 

06 47 64 40 59 29 04 07

06 47 64 40 59 29 04 07

43 28 49 31 58 47 17 45

 

44 28 50 32 57 48 18 46

44 28 50 32 57 48 18 46

26 18 22 52 41 04 27 23

 

25 17 21 51 42 03 27 24

24 27 03 42 51 21 17 25

14 50 30 56 38 64 21 35

 

13 49 30 55 37 63 22 36

36 22 63 37 55 30 49 13

09 57 37 53 61 59 42 20

 

10 58 38 54 61 60 41 19

19 41 60 61 54 38 58 10

01 44 13 33 10 06 25 12

43 28 49 31 58 47 17 45

01 43 14 32 09 05 26 11

11 26 05 09 32 14 43 01

Pair 10/15

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

10 06 25 12 01 44 13 33

58 47 17 45 43 28 49 31

09 05 26 11 01 43 14 34

09 05 26 11 01 43 14 34

61 59 42 20 09 57 37 53

 

61 60 41 19 10 58 38 54

61 60 41 19 10 58 38 54

38 64 21 35 14 50 30 56

 

37 63 22 36 13 49 30 55

37 63 22 36 13 49 30 55

41 04 27 23 26 18 22 52

 

42 03 27 24 25 17 21 51

42 03 27 24 25 17 23 51

58 47 17 45 43 28 49 31

 

57 48 18 46 44 28 59 32

32 59 28 44 46 18 48 57

60 29 03 08 05 48 63 39

 

59 29 04 07 06 47 64 40

40 64 47 06 07 04 29 59

54 40 51 16 34 32 55 62

 

53 39 52 15 33 31 56 62

62 56 31 33 15 52 39 53

19 07 24 02 11 46 36 15

41 04 27 23 26 18 22 52

20 08 23 02 12 45 35 16

16 35 45 12 02 23 08 20

Pair 58/52

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

58 47 17 45 43 28 49 31

10 06 25 12 01 44 13 33

57 48 18 46 44 28 59 32

57 48 18 46 44 28 59 32

60 29 03 08 05 48 63 39

 

59 29 04 07 06 47 64 40

59 29 04 07 06 47 64 40

54 40 51 16 34 32 55 62

 

53 39 52 15 33 31 56 62

53 39 52 15 33 31 56 62

19 07 24 02 11 46 36 15

 

20 08 23 02 12 45 35 16

20 08 23 02 12 45 35 16

10 06 25 12 01 44 13 33

 

09 05 26 11 01 43 14 34

34 14 43 01 11 26 05 09

61 59 42 20 09 57 37 53

 

61 60 41 19 10 58 38 54

61 60 41 19 10 58 38 54

38 64 21 35 14 50 30 56

 

37 63 22 36 13 49 30 55

55 30 49 13 36 22 63 37

41 04 27 23 26 18 22 52

19 07 24 02 11 46 36 15

42 03 27 24 25 17 21 51

51 23 17 25 24 27 03 42

Pair 38/39

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

38 64 21 35 14 50 30 56

54 40 51 16 34 32 55 62

37 63 22 36 13 49 30 55

37 63 22 36 13 49 30 55

41 04 27 23 26 18 22 52

 

42 03 27 24 25 17 21 51

42 03 27 24 25 17 23 51

10 06 25 12 01 44 13 33

 

09 05 26 11 01 43 14 34

09 05 26 11 01 43 14 34

61 59 42 20 09 57 37 53

 

61 60 41 19 10 58 38 54

61 60 41 19 10 58 38 54

54 40 51 16 34 32 55 62

 

53 39 52 15 33 31 56 62

62 56 31 33 15 52 39 53

19 07 24 02 11 46 36 15

 

20 08 23 02 12 45 35 16

16 35 45 12 02 23 08 20

58 47 17 45 43 28 49 31

 

57 48 18 46 44 28 59 32

32 59 28 44 46 18 48 57

60 29 03 08 05 48 63 39

61 59 42 20 09 57 37 53

59 29 04 07 06 47 64 40

40 64 47 06 07 04 29 59

Pair 54/53

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

54 40 51 16 34 32 55 62

38 64 21 35 14 50 30 56

53 39 52 15 33 31 56 62

53 39 52 15 33 31 56 62

19 07 24 02 11 46 36 15

 

20 08 23 02 12 45 35 16

20 08 23 02 12 45 35 16

58 47 17 45 43 28 49 31

 

57 48 18 46 44 28 59 32

57 48 18 46 44 28 59 32

60 29 03 08 05 48 63 39

 

59 29 04 07 06 47 64 40

59 29 04 07 06 47 64 40

38 64 21 35 14 50 30 56

 

37 63 22 36 13 49 30 55

55 30 49 13 36 22 63 37

41 04 27 23 26 18 22 52

 

42 03 27 24 25 17 21 51

51 23 17 25 24 27 03 42

10 06 25 12 01 44 13 33

 

09 05 26 11 01 43 14 34

34 14 43 01 11 26 05 09

61 59 42 20 09 57 37 53

60 29 03 08 05 48 63 39

61 60 41 19 10 58 38 54

54 38 58 10 19 41 60 61

Pair 61/62

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

61 59 42 20 09 57 37 53

60 29 03 08 05 48 63 39

61 60 41 19 10 58 38 54

61 60 41 19 10 58 38 54

10 06 25 12 01 44 13 33

 

09 05 26 11 01 43 14 34

09 05 26 11 01 43 14 34

41 04 27 23 26 18 22 52

 

42 03 27 24 25 17 21 51

42 03 27 24 25 17 23 51

38 64 21 35 14 50 30 56

 

37 63 22 36 13 49 30 55

37 63 22 36 13 49 30 55

60 29 03 08 05 48 63 39

 

59 29 04 07 06 47 64 40

40 64 47 06 07 04 29 59

58 47 17 45 43 28 49 31

 

57 48 18 46 44 28 59 32

32 59 28 44 46 18 48 57

19 07 24 02 11 46 36 15

 

20 08 23 02 12 45 35 16

16 35 45 12 02 23 08 20

54 40 51 16 34 32 55 62

38 64 21 35 14 50 30 56

53 39 52 15 33 31 56 62

62 56 31 33 15 52 39 53

Pair 60/56

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

60 29 03 08 05 48 63 39

61 59 42 20 09 57 37 53

59 29 04 07 06 47 64 40

59 29 04 07 06 47 64 40

58 47 17 45 43 28 49 31

 

57 48 18 46 44 28 59 32

57 48 18 46 44 28 59 32

19 07 24 02 11 46 36 15

 

20 08 23 02 12 45 35 16

20 08 23 02 12 45 35 16

54 40 51 16 34 32 55 62

 

53 39 52 15 33 31 56 62

53 39 52 15 33 31 56 62

61 59 42 20 09 57 37 53

 

61 60 41 19 10 58 38 54

54 38 58 10 19 41 60 61

10 06 25 12 01 44 13 33

 

09 05 26 11 01 43 14 34

34 14 43 01 11 26 05 09

41 04 27 23 26 18 22 52

 

42 03 27 24 25 17 21 51

51 23 17 25 24 27 03 42

38 64 21 35 14 50 30 56

54 40 51 16 34 32 55 62

37 63 22 36 13 49 30 55

55 30 49 13 36 22 63 37

Pair 41/31

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

41 04 27 23 26 18 22 52

19 07 24 02 11 46 36 15

42 03 27 24 25 17 21 51

42 03 27 24 25 17 23 51

38 64 21 35 14 50 30 56

 

37 63 22 36 13 49 30 55

37 63 22 36 13 49 30 55

61 59 42 20 09 57 37 53

 

61 60 41 19 10 58 38 54

61 60 41 19 10 58 38 54

10 06 25 12 01 44 13 33

 

09 05 26 11 01 43 14 34

09 05 26 11 01 43 14 34

19 07 24 02 11 46 36 15

 

20 08 23 02 12 45 35 16

16 35 45 12 02 23 08 20

54 40 51 16 34 32 55 62

 

53 39 52 15 33 31 56 62

62 56 31 33 15 52 39 53

60 29 03 08 05 48 63 39

 

59 29 04 07 06 47 64 40

40 64 47 06 07 04 29 59

58 47 17 45 43 28 49 31

10 06 25 12 01 44 13 33

57 48 18 46 44 28 59 32

32 59 28 44 46 18 48 57

Pair 19/33

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

19 07 24 02 11 46 36 15

41 04 27 23 26 18 22 52

20 08 23 02 12 45 35 16

20 08 23 02 12 45 35 16

54 40 51 16 34 32 55 62

 

53 39 52 15 33 31 56 62

53 39 52 15 33 31 56 62

60 29 03 08 05 48 63 39

 

59 29 04 07 06 47 64 40

59 29 04 07 06 47 64 40

58 47 17 45 43 28 49 31

 

57 48 18 46 44 28 59 32

57 48 18 46 44 28 59 32

41 04 27 23 26 18 22 52

 

42 03 27 24 25 17 21 51

51 23 17 25 24 27 03 42

38 64 21 35 14 50 30 56

 

37 63 22 36 13 49 30 55

55 30 49 13 36 22 63 37

61 59 42 20 09 57 37 53

 

61 60 41 19 10 58 38 54

54 38 58 10 19 41 60 61

10 06 25 12 01 44 13 33

58 47 17 45 43 28 49 31

09 05 26 11 01 43 14 34

34 14 43 01 11 26 05 09

Pair 13/07

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

13 33 01 44 25 12 10 06

49 31 43 28 17 45 58 47

14 34 01 43 26 11 09 05

14 34 01 43 26 11 09 05

37 53 09 57 42 20 61 59

 

38 54 10 58 41 19 61 60

38 54 10 58 41 19 61 60

30 56 14 50 21 35 38 64

 

30 55 13 49 22 36 37 63

30 55 13 49 22 36 37 63

22 52 26 18 27 23 41 04

 

21 51 25 17 27 24 42 03

21 51 25 17 27 24 42 03

49 31 43 28 17 45 58 47

 

50 32 44 28 16 46 57 48

48 57 46 16 28 44 32 50

63 39 05 48 03 08 60 29

 

64 40 06 47 04 07 59 29

29 59 07 04 47 06 40 64

55 62 34 32 51 16 54 40

 

56 62 33 31 52 15 53 39

39 53 15 52 31 33 62 56

36 15 11 46 24 02 19 07

22 52 26 18 27 23 41 04

35 16 12 45 23 02 20 08

08 20 02 23 45 12 16 35

Pair 49/04

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

49 31 43 28 17 45 58 47

13 33 01 44 25 12 10 06

50 32 44 28 16 46 57 48

50 32 44 28 16 46 57 48

63 39 05 48 03 08 60 29

 

64 40 06 47 04 07 59 29

64 40 06 47 04 07 59 29

55 62 34 32 51 16 54 40

 

56 62 33 31 52 15 53 39

56 62 33 31 52 15 53 39

36 15 11 46 24 02 19 07

 

35 16 12 45 23 02 20 08

35 16 12 45 23 02 20 08

13 33 01 44 25 12 10 06

 

14 34 01 43 26 11 09 05

05 09 11 26 43 01 34 14

37 53 09 57 42 20 61 59

 

38 54 10 58 41 19 61 60

60 61 19 41 58 10 54 38

30 56 14 50 21 35 38 64

 

30 55 13 49 22 36 37 63

63 37 36 22 49 13 55 30

22 52 26 18 27 23 41 04

36 15 11 46 24 02 19 07

21 51 25 17 27 24 42 03

03 42 24 27 17 25 51 21

Pair 30/29

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

30 56 14 50 21 35 38 64

55 62 34 32 51 16 54 40

30 55 13 49 22 36 37 63

30 55 13 49 22 36 37 63

22 52 26 18 27 23 41 04

 

21 51 25 17 27 24 42 03

21 51 25 17 27 24 42 03

13 33 01 44 25 12 10 06

 

14 34 01 43 26 11 09 05

14 34 01 43 26 11 09 05

37 53 09 57 42 20 61 59

 

38 54 10 58 41 19 61 60

38 54 10 58 41 19 61 60

55 62 34 32 51 16 54 40

 

56 62 33 31 52 15 53 39

39 53 15 52 31 33 62 56

36 15 11 46 24 02 19 07

 

35 16 12 45 23 02 20 08

08 20 02 23 45 12 16 35

49 31 43 28 17 45 58 47

 

50 32 44 28 16 46 57 48

48 57 46 16 28 44 32 50

63 39 05 48 03 08 60 29

37 53 09 57 42 20 61 59

64 40 06 47 04 07 59 29

29 59 07 04 47 06 40 64

Pair 55/59

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

55 62 34 32 51 16 54 40

30 56 14 50 21 35 38 64

56 62 33 31 52 15 53 39

56 62 33 31 52 15 53 39

36 15 11 46 24 02 19 07

 

35 16 12 45 23 02 20 08

35 16 12 45 23 02 20 08

49 31 43 28 17 45 58 47

 

50 32 44 28 16 46 57 48

50 32 44 28 16 46 57 48

63 39 05 48 03 08 60 29

 

64 40 06 47 04 07 59 29

64 40 06 47 04 07 59 29

30 56 14 50 21 35 38 64

 

30 55 13 49 22 36 37 63

63 37 36 22 49 13 55 30

22 52 26 18 27 23 41 04

 

21 51 25 17 27 24 42 03

03 42 24 27 17 25 51 21

13 33 01 44 25 12 10 06

 

14 34 01 43 26 11 09 05

05 09 11 26 43 01 34 14

37 53 09 57 42 20 61 59

63 39 05 48 03 08 60 29

38 54 10 58 41 19 61 60

60 61 19 41 58 10 54 38

Pair 37/40

Root Vertical Binary

Quality Matrix Root

Horizontal Binary

Balance Matrix

37 53 09 57 42 20 61 59

63 39 05 48 03 08 60 29

38 54 10 58 41 19 61 60

38 54 10 58 41 19 61 60

13 33 01 44 25 12 10 06

 

14 34 01 43 26 11 09 05

14 34 01 43 26 11 09 05

22 52 26 18 27 23 41 04

 

21 51 25 17 27 24 42 03

21 51 25 17 27 24 42 03

30 56 14 50 21 35 38 64

 

30 55 13 49 22 36 37 63

30 55 13 49 22 36 37 63

63 39 05 48 03 08 60 29

 

64 40 06 47 04 07 59 29

29 59 07 04 47 06 40 64

49 31 43 28 17 45 58 47

 

50 32 44 28 16 46 57 48

48 57 46 16 28 44 32 50

36 15 11 46 24 02 19 07

 

35 16 12 45 23 02 20 08

08 20 02 23 45 12 16 35

55 62 34 32 51 16 54 40

30 56 14 50 21 35 38 64

56 62 33 31 52 15 53 39

39 53 15 52 31 33 62 56

Pair 63/64

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

63 39 05 48 03 08 60 29

37 53 09 57 42 20 61 59

64 40 06 47 04 07 59 29

64 40 06 47 04 07 59 29

49 31 43 28 17 45 58 47

 

50 32 44 28 16 46 57 48

50 32 44 28 16 46 57 48

36 15 11 46 24 02 19 07

 

35 16 12 45 23 02 20 08

35 16 12 45 23 02 20 08

55 62 34 32 51 16 54 40

 

56 62 33 31 52 15 53 39

56 62 33 31 52 15 53 39

37 53 09 57 42 20 61 59

 

38 54 10 58 41 19 61 60

60 61 19 41 58 10 54 38

13 33 01 44 25 12 10 06

 

14 34 01 43 26 11 09 05

05 09 11 26 43 01 34 14

22 52 26 18 27 23 41 04

 

21 51 25 17 27 24 42 03

03 42 24 27 17 25 51 21

30 56 14 50 21 35 38 64

55 62 34 32 51 16 54 40

30 55 13 49 22 36 37 63

63 37 36 22 49 13 55 30

Pair 22/47

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

22 52 26 18 27 23 41 04

36 15 11 46 24 02 19 07

21 51 25 17 27 24 42 03

21 51 25 17 27 24 42 03

30 56 14 50 21 35 38 64

 

30 55 13 49 22 36 37 63

30 55 13 49 22 36 37 63

37 53 09 57 42 20 61 59

 

38 54 10 58 41 19 61 60

38 54 10 58 41 19 61 60

13 33 01 44 25 12 10 06

 

14 34 01 43 26 11 09 05

14 34 01 43 26 11 09 05

36 15 11 46 24 02 19 07

 

35 16 12 45 23 02 20 08

08 20 02 23 45 12 16 35

55 62 34 32 51 16 54 40

 

56 62 33 31 52 15 53 39

39 53 15 52 31 33 62 56

63 39 05 48 03 08 60 29

 

64 40 06 47 04 07 59 29

29 59 07 04 47 06 40 64

49 31 43 28 17 45 58 47

13 33 01 44 25 12 10 06

50 32 44 28 16 46 57 48

48 57 46 16 28 44 32 50

Pair 36/06

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

36 15 11 46 24 02 19 07

22 52 26 18 27 23 41 04

35 16 12 45 23 02 20 08

35 16 12 45 23 02 20 08

55 62 34 32 51 16 54 40

 

56 62 33 31 52 15 53 39

56 62 33 31 52 15 53 39

63 39 05 48 03 08 60 29

 

64 40 06 47 04 07 59 29

64 40 06 47 04 07 59 29

49 31 43 28 17 45 58 47

 

50 32 44 28 16 46 57 48

50 32 44 28 16 46 57 48

22 52 26 18 27 23 41 04

 

21 51 25 17 27 24 42 03

03 42 24 27 17 25 51 21

30 56 14 50 21 35 38 64

 

30 55 13 49 22 36 37 63

63 37 36 22 49 13 55 30

37 53 09 57 42 20 61 59

 

38 54 10 58 41 19 61 60

60 61 19 41 58 10 54 38

13 33 01 44 25 12 10 06

49 31 43 28 17 45 58 47

14 34 01 43 26 11 09 05

05 09 11 26 43 01 34 14

Pair 25/46

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

25 12 10 06 13 33 01 44

17 45 58 47 49 31 43 28

26 11 09 05 14 34 01 43

26 11 09 05 14 34 01 43

42 20 61 59 37 53 09 57

 

41 19 61 60 38 54 10 58

41 19 61 60 38 54 10 58

21 35 38 64 30 56 14 50

 

22 36 37 63 30 55 13 49

22 36 37 63 30 55 13 49

27 23 41 04 22 52 26 18

 

27 24 42 03 21 51 25 17

27 24 42 03 21 51 25 17

17 45 58 47 49 31 43 28

 

18 46 57 48 50 32 44 28

28 44 32 50 48 57 46 18

03 08 60 29 63 39 05 48

 

04 07 59 29 64 40 06 47

47 06 40 64 29 59 07 04

51 16 54 40 55 62 34 32

 

52 15 53 39 56 62 33 31

31 33 62 56 39 53 15 52

24 02 19 07 36 15 11 46

27 23 41 04 22 52 26 18

23 02 20 08 35 16 12 45

45 12 16 35 08 20 02 23

Pair 17/18

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

17 45 58 47 49 31 43 28

25 12 10 06 13 33 01 44

18 46 57 48 50 32 44 28

18 46 57 48 50 32 44 28

03 08 60 29 63 39 05 48

 

04 07 59 29 64 40 06 47

04 07 59 29 64 40 06 47

51 16 54 40 55 62 34 32

 

52 15 53 39 56 62 33 31

52 15 53 39 56 62 33 31

24 02 19 07 36 15 11 46

 

23 02 20 08 35 16 12 45

23 02 20 08 35 16 12 45

25 12 10 06 13 33 01 44

 

26 11 09 05 14 34 01 43

43 01 34 14 05 09 11 26

42 20 61 59 37 53 09 57

 

41 19 61 60 38 54 10 58

58 10 54 38 60 61 19 41

21 35 38 64 30 56 14 50

 

22 36 37 63 30 55 13 49

49 13 55 30 63 37 36 22

27 23 41 04 22 52 26 18

24 02 19 07 36 15 11 46

27 24 42 03 21 51 25 17

17 25 51 21 03 42 24 27

Pair 21/48

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

21 35 38 64 30 56 14 50

51 16 54 40 55 62 34 32

22 36 37 63 30 55 13 49

22 36 37 63 30 55 13 49

27 23 41 04 22 52 26 18

 

27 24 42 03 21 51 25 17

27 24 42 03 21 51 25 17

25 12 10 06 13 33 01 44

 

26 11 09 05 14 34 01 43

26 11 09 05 14 34 01 43

42 20 61 59 37 53 09 57

 

41 19 61 60 38 54 10 58

41 19 61 60 38 54 10 58

51 16 54 40 55 62 34 32

 

52 15 53 39 56 62 33 31

31 33 62 56 39 53 15 52

24 02 19 07 36 15 11 46

 

23 02 20 08 35 16 12 45

45 12 16 35 08 20 02 23

17 45 58 47 49 31 43 28

 

18 46 57 48 50 32 44 28

28 44 32 50 48 57 46 18

03 08 60 29 63 39 05 48

42 20 61 59 37 53 09 57

04 07 59 29 64 40 06 47

47 06 40 64 29 59 07 04

Pair 51/57

Root Vertical Binary

Quality Matrix

Root Horizontal Binary

Balance Matrix

51 16 54 40 55 62 34 32

21