Japan has influenced American architecture for over a century now. Frank Lloyd Wright was an avid collector and broker of Japanese prints - to tide him over those dry spells in his career. It also has a deep influence in the Greene & Greene bungalow style here in Pasadena, and of course in much of modern architecture. The zen temples of Japan, such as the Ryoan Ji Garden in Kyoto (picture above), are spectacular in their rendition of simplicity, as well as an expression of the deep structure of the Fibonacci series embedded in the proportional principles of nature. This system of proportion is derived from understanding natural patterns, and is known in Western culture as "The Golden Mean".
However, it goes beyond the aesthetic now, and fundamental principles applied in the design of structures in the Japanese tradition reflect a necessary conservation of all means and energies. This is discussed in an excellent article by Azby Brown, a native of New Orleans, Louisiana, is an artist and designer who has lived in Japan since 1985. On the faculty of the Kanazawa Institute of Technology, he is the director of the KIT Future Design Institute in Tokyo. His essay, "Bent by the Sun" describes the principles of sustainability as they have evolved in Japanese culture over thousands of years.
A snippet from the slide show (below) uses very simple diagrams to illustrate the principles that Brown has observed during his time in Japan. He emphasizes the approach to "multiform solutions" and efficient processes. These traditions are being broken down by Japan's industrial revolution in the late 19th century, ironically about the time its influence in America was ascendant, so these lessons need to be preserved.