
Hexagrams ijing or iching are a
complex of symbols of the Chinese Classical Book of Changes in which there is a
certain sequence of symbols, namely hexagrams have serial numbers which
form sequence.
This sequence has no any logic substantiations, that is no mathematical
calculations or geometrical constructions can explain law according to which the
sequence is constructed. It is known that the sequence has been established by
the legendary King Wen or the governor of ancient China, and also it is
considered that the sequence of hexagrams ijing possesses esoteric sense in
which metaphysical laws of the world are ciphered, but however the logic essence
and mathematical principles of sequence
(the King Wen's sequence of hexagrams) are unknown.
In some cases researchers of the Book of Changes consider that hexagrams ijing
are randomized, but in comments of the Book of Changes is told that King Wen has
found sequence of hexagrams in the wonderful image as a result of a combination
of magic squares. Therefore there should be a logic law according to which
hexagrams ijing are organized.
In particular look the information on pages of this website in section which
has the name chronology where there are
numerical ratio and calculations which confirm that there is a mathematical
order according to which King Wen has established sequence of the Book of
Changes. The shown numerical ratio are not a substantiation of concrete
mathematical principles and laws, but actually are acknowledgement of a
hypothesis on existence of mathematical and geometrical algorithms according to
which the order of symbols in the Book of Changes is organized.
If to analyze sequence of hexagrams ijing then it is possible to see system
which is shown on the scheme:
Numbers on the scheme designate serial numbers of
hexagrams. Serial numbers and corresponding hexagrams ijing form pairs which possess property of reflection, namely pairs are reflected concerning each other or are turned concerning each other on 180 degrees. For example, 3rd hexagram forms the reflected pair with 4th hexagram. Symbols of hexagrams ijing look below on this page. All the shown pairs possess property of reflection except for 12, 2728, 2930, 6162. But these hexagrams form pairs which property is inversion of lines. For example, in 1st hexagram all positions are occupied by the entire lines, and in 2nd hexagram all positions are occupied by the break lines, namely there are inversions or changes of lines. Inverse pairs are designated on the scheme by sign X. Property of inversion also is in quadras in which pairs are incorporated. For example, 34 hexagrams form the quadra with 4950 hexagrams as positions are occupied by the entire lines in one pair and corresponding positions are occupied by the break lines in the second pair. Quadras are designated on the scheme by arches. Besides there are pairs in which hexagrams ijing possess both property of reflection, and property of inversion. Such pairs are designated by sign Y. 

Serial numbers on the scheme are incorporated with the conditional image of a
human body that symbolizes esoteric sense according to which it is possible to
speak that general laws of the universe and fundamental laws of the world are
ciphered in sequence of hexagrams ijing, and including metaphysical structures
of a human body are ciphered. And also it is possible to speak that the sequence
of the Book of Changes corresponds with laws of world harmony and corresponds to
a building of the Universe.
From the view of Indian philosophy it is possible to speak that
hexagrams ijing designate chakras or power points of a human body though
precisely do not coincide with traditional Indian chakras, but certainly are a
row of symbols which designate structural ratio of power points, and designate
points in more detail rather than Indian chakras.
From the view of alchemy it is possible to speak that the sequence of
hexagrams ijing is the scheme for alchemical management (control) of a human
body, and also is the scheme for transformations of substances in alchemy.
From the view of mythology it is possible to speak that the order of
hexagrams ijing is the World Tree (the Universe Tree) or the Universe Ladder
which connects the ground and the sky.
There can be various schemes, and including various configurations
within magic squares, according to which the consecutive order of hexagrams in
the Book of Changes ijing is organized, but also sequence of hexagrams can be
considered as esoteric system which corresponds with chakras and metaphysical
structures of a human body, and also corresponds with laws of world harmony and
with a structural building of the Universe.
Below pairs and quadras of hexagrams are shown, and also corresponding
physiognomic symbols which are connected with hexagrams and too form sequence
which corresponds with mathematical algorithm in the Book of Changes ijing. And
in essence the sequence of physiognomic symbols corresponds with the esoteric
system of harmonious laws in the Universe.
1. 2.
3. 4.  49. 50.
5. 6.  35. 36.
7. 8.  13. 14.
9. 10.  15. 16.
11. 12.
17. 18.
19. 20.  33. 34.
21. 22.  47. 48.
23. 24.  43. 44.
25. 26.  45. 46.
27. 28.
29. 30.
31. 32.  41. 42.
37. 38.  39. 40.
51. 52.  57. 58.
53. 54.
55. 56.  59. 60.
61. 62.
63. 64.
The additional information on interrelations and parities of hexagrams ijing, and more detailed information on human emotions look on pages of this website in section which has the name concepts of the canon of changes.
The following page organizes 64 hexagrams ijing in five groups according to hexagonal symbols which are a basis of ancient mantic systems, and which allow to correlate hexagrams of the Books of Changes ijing to astrological signs on the Chinese zodiac.
