The Koch snowflake is a fractal curve and a well-known example of a mathematical shape that has an infinite perimeter but a finite area. It starts with an equilateral triangle, and in each iteration, smaller triangles are added to the middle of each side, creating a snowflake-like pattern. This process can be repeated indefinitely, leading to increasingly complex shapes. As the iterations continue, the Koch snowflake demonstrates how simple rules can generate intricate designs. It is often used in mathematics to illustrate concepts of infinity, self-similarity, and geometric growth, making it a popular subject in both education and art.