About Mutual Guas

A mutual gua is formed by the mutual intersections of the second, third, fourth, and fifth lines. The ancient sages considered these four lines to be the heart of any six-line gua. A mutual gua is formed by two trigrams. The second, third, and fourth lines of the original gua form the lower, or inner, mutual gua. The third, fourth, and fifth lines form the upper, or outer, mutual gua. Put the lower mutual gua and the upper mutual gua together and a six-line mutual gua is obtained.

Construction Example

For example, let's see the mutual gua formed from Hexagram 39 (Jian or "hardship"):

As shown above, the mutual gua for Hexagram 39 is Hexagram 64 (Wei Ji or "before completion").

Tree of Mutual Guas

Each hexagram (white background) is grouped under its mutual gua (amber background). These mutual guas themselves are grouped under their own mutual guas (dark amber background), showing how hexagrams converge through successive mutual relationships. Arrows on the right indicate final recursive relationships (guas 1 and 2 are their own mutual guas, while guas 63 and 64 are each other's mutual guas).

Gua Circle

The Gua Circle shows the mutual relationships between the 64 hexagrams. Each hexagram is connected to its mutual gua. The mutual guas are then connected to their mutual guas, forming a circular structure that demonstrates the recursive nature of the mutual guas.