Welcome to waves week.
Waves of various sorts appear frequently in Japanese art, likely because of their dynamic nature. Perhaps the most famous Japanese woodblock print is Katsushika Hokusai's Great Wave. It would be hard to find anyone who has not seen either it or some representation of it.
Note that the waves are represented by only four colors with black (or very dark blue) lines occasionally outlining portions of it. Mt. Fuji almost looks like a wave itself except that it appears to be the one calm, steady part of what is otherwise a very restless picture.
Hokusai's Great Wave is part of his Thirty Six Views of Mt. Fuji series of ukiyo-e woodblock prints. He produced a number of other woodblock series including Eight Views of Waterfalls. The print below comes from that series.
Hokusai's representation of restless water is very different in this painting.
Note the tenkei, the small group of picnickers on the bluff overlooking the waterfall. Tenkei are little elements in landscape scenes that provide subtle points of interest. The boats and fishermen in the Great Wave are tenkei. In seascapes, examples of tenkei may be a small figure of a fisherman mending his nets, a shore bird, or a dolphin breaking the surface of the water. If you use tenkei in your paintings, keep them simple. Remember that the subject isn't the tenkei, it is the seascape/landscape.
Here is another wave picture, this time by Ogata Kōrin (1658-1716), another one of Japan's greatest artists.
This painting, Red Plum, is half of a painting spread across two bi-fold byōbu screens. The predominant color comes from real gold leaf. The swirls in the water are Kōrin's waves.
For reference, here is the entire painting.
Wave patterns also show up in textiles. Here are two examples of wave patterns designed for kimonos.
There are so many different wave patterns in Japanese art and designs that it would be difficult to catalog them all. Thanks go to your fellow student, Cliff Brown, for discovering a little known 3-part book by Mori Yūzan that provides a large number of wave patterns that artists are free to use in their own works. It can be found at Hamonshu: A Japanese Book of Wave and Ripple Designs (1903) (hamonshū -- 波紋集).
Some sample pages from the book are shown below.