Beauty is subjective, and what one person finds beautiful in a katana may differ from another person's opinion. However, there are several katana swords renowned for their exceptional beauty and aesthetic appeal. Here are a few examples of katana swords often regarded as visually stunning:

1. Masamune: Swords attributed to Goro Nyudo Masamune, a legendary Japanese swordsmith from the 13th century, are often considered among the most beautiful katana. Masamune's swords are admired for their elegant and refined designs, impeccable craftsmanship, and the unique characteristics of their hamon (the wavy line pattern along the blade).
2. Soshu Kitae: The Soshu Kitae technique, developed by swordsmiths from the Soshu region, including Masamune, resulted in visually striking blades. The distinct texture and pattern, created by the layering and folding of different types of steel, contribute to the captivating beauty of Soshu Kitae katana.
3. Bizen Osafune: Swords from the Osafune School of Bizen Province are known for their simple and rustic beauty. They often feature a distinct hamon pattern called "midare" with irregular and dynamic fluctuations, adding a unique charm to the blade.
4. Kaga-Ichimonji: The Kaga-Ichimonji style of katana from the Kaga Province showcases intricate and detailed craftsmanship. These swords often feature decorative engravings, ornate tsuba (handguards), and elaborate menuki (hilt ornaments), enhancing their aesthetic appeal.
5. Yamashiro School: The swords crafted by the Yamashiro School in Kyoto are celebrated for their refined elegance and graceful designs. They often feature a gentle sori (curvature), finely detailed horimono (blade engravings), and artistic hamon patterns.

It's important to note that beauty in a katana extends beyond the blade itself. The overall aesthetic appeal can be influenced by factors such as the quality of the fittings, the materials used in the handle and scabbard, and the harmony between the different components of the sword.

Ultimately, the beauty of a katana lies in the eyes of the beholder, and individual preferences may vary. It's advisable to explore various styles and schools of katana to find the one that resonates most with your personal aesthetic tastes.