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

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

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...