The Trigrams and My Interest
My interest in the trigrams of the very ancient Yijing is mostly scholastic. It's the coherent set of philosophies (or canon), derived from these trigrams and what amounts to a mathematical interpretation of everything that have had a more concrete effect on how I go about my life and how I deal with adversity.
The trigrams are many things, but their most interesting characteristics (from a secular point of view) are their direct analogy to the binary numerical system as well as the fact that they (undisputedely) represent the earliest coherent example of humankind's study of semionics:
the philosophical theory of the functions of sign and symbols
The infinite Characteristics of the Trigrams
The first (and less emphasized) of these two characteristics of the trigrams was formally observed by the German mathematician Gottfried Wilhelm Leibniz (the original observation is probably as old as the purported author of the trigrams: FuXi). He, is the creator of the modern binary system of counting, which is the primary framework upon which microprocessor design is based (an important, historical irony).
He noticed that the concept of duality/balance evident in the trigrams' source (the yijing)) as well as the derived related philosophies are directly analogous to the binary system when you substitute 0 for dashed lines (yin - the concept of no motion) and 1 for unbroken lines (yang - the concept of motion / kinetic energy).
The trigrams are meant to be interpreted from the bottom up, so a continuation of this binary analog would have the reader tip the trigrams over to their right side and read them as binary numbers.
The Binary Analog of the Primary Gua
Below is the original horizontal arrangement of the trigrams with their corresponding binary numbers (click on each to view the corresponding SVG diagram):
Extension to the 64 Trigrams of the Yijing
Since, the 8 primary gua are the building blocks upon which the 64 symbols of the Yijing are built (and purportedly, everything), this binary analogy can be extended to all the 64 symbols. This is well known amongst scholars of the Yijing and below is the most famous diagram of this extension by Shao Yong (1011AD - 1077AD):
The numerical significance of the trigrams in sequence is well summarized here. This page also includes a very useful animated image of the entire sequence as a binary progression:
The most complete resource on the subject (that I've read so far) is Alfred Huang's The Numerology of the I Ching (ISBN: 0-89281-811-5)
I was unable to embed the SVG diagrams within the page, which is a shame because the yijing trigrams are an excellent SVG use case. I hope to someday capture all 64 as SVG diagrams so the various, more popular philosophical/visual arrangements can be rendered programatically. Imagine Shao Yong's circular diagram as SVG (talk about an interesting combination of ancient numerology with modern vector graphic technology). It would prove quite a useful tool for avid students of the yijing symbols as well as make for some very interesting patterns.