Pattern

A pattern is a recognisable regularity found in nature, human-made design or abstract ideas. Its defining characteristic is repetition: elements recur in an organised, predictable manner. Patterns may be directly observable through the senses, especially visually, or may emerge only through scientific or mathematical analysis. They manifest across an extraordinary range of contexts, from the geometry of tilings and architectural motifs to the laws of physics, linguistic structures and biological formations. While many natural patterns display approximate repetition influenced by chaos and complexity, others demonstrate remarkable symmetry or fractal organisation.
Patterns have deep foundations in mathematics, which is often described as the study of regularities. Scientific theories similarly explain and predict recurring phenomena, demonstrating the far-reaching role of patterns in understanding the world. In the decorative arts, patterns form the basis of ornamental design across ceramics, textiles and architectural surfaces, providing both aesthetic and structural coherence.

Patterns in Nature

Nature offers countless examples of patterns ranging from simple symmetries to intricate fractal geometries. These emerge from physical laws, biological processes and interactions between energy and matter, often producing complex dynamic forms.
Symmetry
Symmetry is one of nature’s most widespread forms of pattern. Many animals exhibit bilateral (reflection) symmetry, which supports efficient movement. Plants and static organisms such as sea anemones often display radial or rotational symmetry. Fivefold symmetry characterises echinoderms, including starfish, sea urchins and sea lilies. Among non-living systems, snowflakes exhibit intricate symmetrical branching, each one unique due to subtle variations in formation conditions. Crystals form in specific geometric habits such as cubic or octahedral structures, though they cannot exhibit fivefold symmetry—an exception found only in quasicrystals.
Spiral Patterns
Spirals occur widely in biological structures. Molluscs such as the nautilus exhibit spiral shell growth, while plants display spiral leaf arrangements or phyllotaxis. Flower heads such as sunflowers and fruit structures like pineapples demonstrate multiple interlocking spirals that optimise packing and growth efficiency.
Chaos, Turbulence and Meanders
Chaos theory explains why many patterns never repeat exactly. Although governed by deterministic laws, systems exhibiting sensitivity to initial conditions produce complex, unpredictable results. Natural forms shaped by chaotic dynamics include turbulent flows, von Kármán vortex streets, and meandering rivers. Such patterns arise through the interplay between energy input and dissipation, generating ever-changing structures.
Waves and Dunes
Waves represent oscillatory patterns that carry energy through a medium such as air or water. Surface waves create shifting, chaotic sea patterns, and when they move across sand, they generate ripple formations. Wind similarly forms dunes, creating large-scale repeating patterns shaped by airflow and sediment properties.
Foams and Bubbles
Foams obey Plateau’s laws, producing smooth films and constant mean curvature. Bubble and foam structures appear naturally in organisms such as radiolarians, sponges and sea urchins. They demonstrate efficient space-filling properties and arise from physical constraints on surface tension and geometry.
Cracks and Fractures
Crack patterns relieve internal stress within materials. Elastic materials typically break at 120-degree angles, while inelastic materials form 90-degree fractures. Cracking patterns are evident in dried mud, rock formations, tree bark, and in the glaze of aged ceramics and paintings.
Spots and Stripes
Alan Turing’s reaction–diffusion model describes how interacting chemical processes generate spontaneous patterns such as stripes, spots and spirals on animal skin or plumage. These patterns may shift subtly over time, aligning with Turing’s prediction of slow spatiotemporal drift.

Patterns in Art and Architecture

In visual art, patterns organise surfaces through repeated or rhythmically arranged motifs. They appear in drawings, textiles, ceramics, and decorative architecture. Patterns in art need not repeat exactly; they may instead provide an underlying structural rhythm guiding the viewer’s perception.
In architecture, patterns emerge through the repetition of structural elements such as windows, columns and pediments. South Indian temples illustrate fractal-like repetition, with architectural forms repeating at successively smaller scales to create a coherent pyramidal structure.
Mathematically, artistic patterns often involve tessellations, tiling a plane with geometric shapes that meet without overlap or gaps. These patterns underpin both decorative design and theoretical explorations in geometry.

Patterns in Language and Literature

Language offers abundant patterns for linguistic and literary study. Sound patterns appear in rhyme, alliteration and rhythm. Grammatical patterns organise syntax, while semantic and narrative patterns inform imagery, motifs and plot structure. These regularities help researchers analyse the structure, function and aesthetics of spoken and written communication.

Patterns in Science and Mathematics

Mathematics is frequently described as the “science of pattern”. Any numerical sequence that can be modelled by a function represents a mathematical pattern, as does the output of any systematic process. Scientific observations—from planetary motion governed by gravitational equations to daily cycles of sunlight—exemplify consistent natural patterns described by mathematical laws.
The deeper relationship between mathematics and the world has been famously noted for its “unreasonable effectiveness”: mathematical formulations often describe physical patterns with extraordinary precision. Differential equations, for instance, provide powerful tools for modelling the most general empirical phenomena.

Real Patterns

Philosopher Daniel Dennett’s concept of “real patterns” offers an ontological perspective on the status of patterns. Real patterns are those that provide predictive utility and enable efficient information compression. For example, modelling the Earth as having a centre of mass simplifies calculations of its motion while offering accurate predictions. Such a model compresses complex particle interactions into a simpler, effective pattern.

Fractals and Pattern Theory

Fractals are mathematical patterns characterised by scale invariance: their structure remains consistent regardless of magnification level. Natural examples include tree branching, lightning, and coastline boundaries. Despite their apparent complexity, fractals can often be generated using simple rules, such as those found in Lindenmayer systems that model plant growth.
Pattern theory, developed by Ulf Grenander, aims to describe the world through computationally useful pattern structures. By abstracting and formalising patterns, this theory seeks to create frameworks for analysis in fields ranging from image recognition to biological modelling.