The Graphic I Ching
The I Ching may be displayed graphically as a series of columns of six blocks, each block representing a yin or yang line. This is often done when comparing it to the binary number sequence. Another way to arrange the binary sequence is in alternating reversed pairs, along the lines of the “received” (King Wen) sequence. All the above, plus the Mawangdui sequence, Chu Hsi’s sequence (actually a list of all possible changed hexagrams), Wilhelm’s “mystery sequence,” and the Gray code (only one line changes at a time) are displayed below for comparison. Yin is dark, yang is light.
The lack of any obvious pattern to the King Wen sequence tempts me to think that the order may be influenced by the subject of the text, as described in the ninth wing, and is not purely mathematical. However, a compelling system of symmetries in the binary values of the 8x8 “magic square” of hexagrams discovered by Immanuel Olsvanger, described in Zhouyi: A New Translation with Commentary of the Book of Changes by Richard Rutt, makes me think otherwise. See The Foursome Pairs for more details.
Binary (Shao Yong):
Alternating reversed binary: