Pattern

Definition

A pattern is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects that repeat in a predictable manner.

The most basic patterns, called tessellations, are based on repetition and periodicity. A single template, tile, or cell is combined with duplicates without change or modification. For example, simple harmonic oscillators produce repeated patterns of movement.

Other patterns use symmetry, which is a form of finite repetition, instead of translation, which can repeat infinitely. Fractal patterns also use magnification or scaling, giving an effect known as self-similarity or scale invariance. Some plants, like ferns, even generate a pattern using an affine transformation which combines translation, scaling, rotation, and reflection.

Mathematics is commonly described as the “Science of Patterns.” Any sequence of numbers that may be modeled by a mathematical function is considered a pattern. In pattern theory (Grenander 1996),...