Pattern formation refers to the process by which organized structures emerge in nature, often seen in biological systems. This phenomenon can be observed in various contexts, such as the arrangement of animal fur, the growth of plants, or the development of embryos. These patterns arise from interactions between cells, chemicals, and environmental factors, leading to distinct shapes and structures. In mathematics and physics, pattern formation can also be studied through models and simulations. For example, Turing patterns describe how chemical reactions can create spatial patterns, while fractals illustrate self-similar structures at different scales. Understanding these processes helps scientists explain complex natural phenomena and their underlying principles.