Symmetries

Border pattern on my fence

Pretty and simple border pattern at a playground in Brooklyn.

I saw this pretty mandala-ish figure on the lid of a jar…

Border pattern on the subway at Fulton St.

Some of the most beautiful symmetries can be found on the wings of butterflies. Butterflies developed such flamboyant colors and figures for many reasons. One of which is to create a camouflage to protect themselves from predators. Some other species of butterflies developed such brilliant colors to be used in courtship, so that the same species can recognize each other. Finally, certain poisonous butterflies developed colorful patterns to warn prevent predators from eating them by accident.

Not all mandalas are artificially constructed for artistic purposes; they can be constructed naturally as well. The two flowers above have each formed a mandala-image. The petals and stigmas have effectively separated the structure into several sections, and thus they have naturally constructed a mandala of its own.

This is a 12 symmetry type found on bathroom tiles!

Irworobongdo is a Korean folding screen with a highly stylized landscape painting of a sun and moon, five peaks which
always was set behind Eojwa, the king’s royal throne during the Joseon Dynasty. It literally means “Painting of the Sun, Moon and
the Five Peaks” and is also called “Irwoldo” or “Irwolgonryundo”. The sun and moon symbolize the king and queen while
the five peaks denotes a mythical place. The screen serves to display the majesty of the Joseon royal court. <Wikipedia>

Snowflakes are symmetrical because they reflect the internal order of the water molecules as they arrange themselves in the solid state (the process of crystallization). Water molecules in the solid state, such as in ice and snow, form weak bonds (called hydrogen bonds) to one another. These ordered arrangements result in the basic symmetrical, hexagonal shape of the snowflake. In reality, there are many different types of snowflakes (as in the clich¿ that ‘no two snowflakes are alike’); this differentiation occurs because each snowflake is a separate crystal that is subject to the specific atmospheric conditions, notably temperature and humidity, under which it is formed.

Chinese opera performers mainly have two methods of makeup: masks and facial painting. The frequent on-stage change of masks, without the audience noticing, is a special technique, known as changing faces.  The funny thing is that, each of the faces should be symmetric and different from each other to show different characteristics.

In Chinese philosophy, the concept of yin-yang , which is often called “yin and yang”, is used to describe how seemingly opposite or contrary forces are interconnected and interdependent in the natural world; and, how they give rise to each other as they interrelate to one another. Many natural dualities (such as male and female, light and dark, high and low, hot and cold, water and fire, life and death, and so on) are thought of as physical manifestations of the yin-yang concept. The concept lies at the origins of many branches of classical Chinese science and philosophy, as well as being a primary guideline of traditional Chinese medicine,  and a central principle of different forms of Chinese martial art and exercise.

This is a character representing ” marriage” and only can be seen in a wedding in China. It is symmetric because it shows the connective relation between the bride and bridegroom. The half of the character can be recognized as one of the spouse.

This is a character representing ” marriage” and only can be seen in a wedding in China. It is symmetric because it shows the connective relation between the bride and bridegroom. The half of the character can be recognized as one of the spouse.