The wave-like pattern often seen on the edge of a katana blade is called a hamon. The hamon is a result of the differential hardening process used in traditional Japanese sword-making, specifically in the creation of katana blades. The purpose of the hamon is primarily aesthetic but can also provide insights into the blade's construction and quality.

The differential hardening process involves heating the blade and then quenching it in water or oil. The edge of the blade, which is made of high-carbon steel, hardens more quickly and becomes extremely hard. The back of the blade, known as the spine, which is made of lower-carbon steel, remains relatively softer and more flexible.

During the quenching process, a clay mixture is applied to the blade. Thicker layers of clay are usually applied to the spine and thinner layers or no clay at all on the edge. This creates a temperature differential during quenching, causing the edge to cool more rapidly, resulting in the hardening of the edge while the spine cools more slowly, maintaining its relative softness.

The hamon, or the wave-like pattern, is the visible line that separates the hardened edge from the softer spine. It is formed by the transformation of the steel's crystal structure during the differential hardening process. The appearance of the hamon is influenced by factors such as the clay mixture, quenching technique, and the skill of the swordsmith.

The hamon is highly valued in traditional Japanese sword craftsmanship as a mark of the sword's authenticity and quality. It is also considered a visually striking and beautiful feature, often enhancing the overall aesthetic appeal of the katana. Different types of hamon patterns can be found, such as straight, wavy, or irregular, each with its own unique charm.

While the hamon primarily serves as a decorative element, it also indicates the craftsmanship and skill of the swordsmith in achieving the desired hardening and tempering of the blade.