Pattern

A pattern is a regularity or repeating arrangement that can be observed in objects, processes, or data. It implies an underlying order or rule that makes a sequence or structure predictable to some degree. Patterns can be visual, musical, spatial, temporal, or abstract, and they often arise from simple rules or interactions.

In nature, patterns appear in forms such as the stripes on animals, the spiral arrangement of leaves (phyllotaxis), tessellations in minerals, and the self-organizing structures produced by reaction-diffusion systems. In mathematics, patterns are studied as sequences, symmetries, and fractals, where self-similarity and recursive rules generate complex forms from simple rules.

In science and engineering, pattern formation explains how complex structures emerge from underlying dynamics. Pattern recognition and pattern mining are key tasks in data analysis, enabling classification, forecasting, and anomaly detection. In computing, pattern matching and regular expressions identify or manipulate strings by matching predefined templates. Pattern languages and design patterns provide reusable solutions to recurring problems in software and system design.

In everyday use, recognizing patterns supports learning, planning, and problem solving by allowing generalization from past experience. Conversely, pattern perception can be misleading if random data produce illusory regularities.

Overall, a pattern is any regular or describable structure that helps to understand, predict, or reproduce phenomena across disciplines.