Pattern formation refers to the process by which organized structures emerge in biological systems. This phenomenon can be observed in various contexts, such as the arrangement of animal fur, the distribution of leaves on a plant, or the formation of shells in marine organisms. These patterns often arise from simple rules governing interactions at a local level, leading to complex and beautiful designs. In mathematics and physics, pattern formation is studied through models that describe how small changes can lead to significant patterns. For example, the Turing model explains how chemical reactions can create spatial patterns, while fractals illustrate self-similar structures in nature. Understanding these processes helps scientists uncover the underlying principles of organization in both living and non-living systems.