Forma, Vol. 27 (No. 1), pp. 5569, 2012

A Coding-Theoretical Approach to Analyzing Sequential Patterns of the Sixty-Four Hexagrams in the I Ching

Kazuya Hayata

Department of Socio-Informatics, Sapporo Gakuin University, Ebetsu 069-8555, Japan
E-mail address:

(Received May 10, 2011; Accepted March 16, 2012)

Abstract. The sequential patterns of the sixty-four hexagrams in the I Ching (the Book of Changes) are analyzed by calculating a divergence between adjacent hexagrams. Geometrically, the divergence is equivalent to the Hamming distance between nodes on a six-dimensional hypercube. Detailed comparisons are made between results for the received ordering of the hexagrams and those for other orderings currently available. Emphasis is on the finding that the received order possesses a sophisticated mathematical structure, suggesting at the same time that it would hold great significance as an integral whole of a human archetype.

Keywords: City-Block Distance, Hamming Distance, Hypercube, I Ching Mandala, Sixty-Four Hexagrams

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