ancient Chinese developed several systems for mapping their five
elements to illustrate the key relationships among them. Ancient diagramming started with divination, which was the main purpose of the I Ching (Yijing), or "book of changes." The I Ching created a special way to decipher the universe that incorporated three parts: xiang (images), shu (numbers), and li (meanings). The original diagrams for divination were called yao. These methods of diagramming were later known in the Xiangshu (image numbers) school as tu (diagrams).
The most basic diagram comes from the points of the compass
. The five elements are associated with the four cardinal points plus the center of the compass. Sun Tzu used this same compass arrangement, but the center of his system was "mission" rather than "earth." (Note: This diagram shows today's "After Heaven" arrangement while Sun Tzu used the "Before Heaven" arrangement explained in other articles on this site.)
The Five Elements were also arranged in a circle to show the "Creation Cycle" as a pentagram. Water creates wood by growing trees. Wood creates fire. Fire creates earth by transforming wood to ash. Earth creates metal, which is why metal is mined from the earth. Metal creates water, as we can see by condensation on metal surfaces. Sun Tzu used different elements, but he adopted this same pattern of one element creating or transforming from one to another.
There is another common mapping of the Five Elements that is important in Sun Tzu's work. This is the "Destruction Cycle" as a five-pointed star pattern. Water destroys fire. Fire destroys metal by melting it. Metal destroys wood by cutting it. Wood destroys earth by transforming it to wood through its roots. Earth destroys water by absorbing it. When Sun Tzu's elements are arranged in the Creation Cycle, as similar star emerges when you create the cycle whereby one element destroys or controls another.
Interestingly, Sun Tzu use the previous two maps in other ways. The "creation" map is used to show to flow of resources and costs from one element to another and it reverse to show the flow of rewards. The "destruction" map is used to show the flow of information (and the types of "spies") and its reverse to show the most common mistakes in using the elements.
Except for the flow of information, which is covered in detail in his chapter on "Using Spies," most of these patterns are referenced only generally because Sun Tzu expected his readers to be familiar with them and their use.