A pattern, from the French patron, is a type of theme of recurring events of or objects, sometimes referred to as elements of a set. These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, Pattern matching is the act of checking for the presence of the constituents of a pattern, whereas the detecting for underlying patterns is referred to as pattern recognition.
The most basic patterns are based on repetition and periodicity. A single template, or cell, is combined with duplicates without change or modification. For example, simple harmonic oscillators produce repeated patterns of movement. Computer science, ethnology, and psychology are fields which study patterns. A recurring pattern in a piece of art is referred to as a motif.
The golden ratio(approximately 1.618) is found frequently in nature. It is defined by two numbers, that form a ratio such that (a+b)/a = a/b (a/b being the golden ratio). This pattern was exploited by Leonardo da Vinci in his art. The golden ratio can be seen in nature, from the spirals of flowers to the symmetry of the human body (as expressed in Da Vinci's Vitruvian Man, one of the most referenced and reproduced works of art today. This is still used by many artists).
"Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern."
Alfred North Whitehead (1861-1947), English philosopher and mathematician. Dialogues, June 10, 1943.