Patterns refer to regularities or repeated structures that can be observed in various phenomena, such as in nature, society, and mathematics. Research in patterns focuses on identifying, analyzing, and understanding the underlying structures and relationships that define these regularities. In mathematics, patterns can be found in sequences, shapes, and numbers, leading to the development of mathematical principles and theories. In nature, patterns are prevalent in natural formations, such as the spirals in shells or the symmetry in flowers. In society, patterns can be observed in trends, behaviors, and cultural phenomena. Research in patterns aims to uncover the underlying mechanisms that give rise to these regularities and to understand their significance in different contexts. By studying patterns, researchers can gain insights into complex systems, make predictions about future outcomes, and develop innovative solutions to problems.