Pattern

A pattern is a regularity found in the physical world, in human-made designs, or within abstract ideas. These regularities occur because the elements of a pattern repeat in a logical and predictable manner. Patterns can be observed directly through our senses, such as seeing a visual design on a piece of fabric. However, abstract patterns in fields like mathematics, science, or language often require careful analysis to detect.

In essence, a pattern provides an organizing structure that allows us to understand complex information.

In nature, patterns are widespread but often appear chaotic or rarely repeat exactly. One major type of natural pattern is symmetry, where parts of an object match or balance each other. Animals that move typically exhibit bilateral symmetry, which is a mirror-like arrangement that favors movement. Many plants and static animals, such as sea anemones, display radial or rotational symmetry.

Other organisms, like starfish and sea urchins, show fivefold symmetry. Even non-living things like snowflakes display striking sixfold symmetry, with each arm recording unique crystallization conditions.

Another common natural occurrence is the spiral pattern. These can be seen in the body plans of molluscs like the nautilus. Plants also use spirals in their phyllotaxis, which is the arrangement of leaves around a stem. You can also find these patterns in the heads of sunflowers or the structure of a pineapple.

Beyond spirals, nature produces patterns through waves, foams, and cracks. Waves carry energy through a medium like air or water, creating surface patterns on the sea. Wind passing over sand creates ripples or larger dunes.

Cracks form in materials like mud or rocks to relieve stress. The angle of these cracks can even tell us if a material is elastic or inelastic.

Mathematics is frequently described as the "Science of Pattern" because it seeks to identify regularities. A mathematical pattern can be any sequence of numbers modeled by a function. One highly complex type of pattern is the fractal. Fractals are scale-invariant, meaning the shape remains similar regardless of how much you magnify it.

This property is known as self-similarity. Natural examples include the shapes of trees or the jagged edges of coastlines. While these patterns look infinitely complex, they can often be produced by very simple mathematical rules.

In the realm of human design, patterns serve both decorative and structural purposes. In the decorative arts, patterns are used in ceramics, textiles, and wallpaper to create ornamental designs. In mathematics, a specific type of tiling is called a tessellation. This occurs when geometric shapes, or tiles, cover a plane with no overlaps and no gaps.

Architects also use patterns by repeating motifs like windows, columns, or pediments. Some structures, such as temples in South India, use a fractal-like approach where elements repeat at different scales.

This can create a sense of organized complexity in a large building.

Scientists use patterns to explain and predict the behavior of the universe. For instance, the rising and falling of the sun is a pattern caused by the Earth's rotation. The moon's path through the sky is a predictable pattern resulting from its orbit. Even complex phenomena like turbulence or vortex streets follow mathematical structures. Chaos theory suggests that while physics is deterministic, tiny changes in starting conditions can cause natural patterns to never repeat exactly.

These regularities allow scientists to use differential equations to describe the most general patterns of the universe.

Philosophical and psychological studies also explore the impact of patterns. Philosopher Daniel Dennett discussed "real patterns," which are patterns that provide predictive utility and help compress information. For example, the center of gravity is a real pattern because it allows us to predict how planets move. Additionally, research into fractal-based design suggests that these patterns can affect human wellbeing. Studies show that including natural, fractal patterns in human-made environments can impact how people feel, sometimes helping to lower stress through engagement and relaxation.