|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
Top line is least significant bit for binary
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
Bottom line is least significant bit for binary
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
To transform between these two arrangements
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.
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...