Patterns in nature

Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.

Early Greek philosophers like Plato, Pythagoras and Empedocles studied pattern, trying to explain order in nature. The modern understanding of visible patterns developed gradually over time.

In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth.

In the 20th century, the English mathematician Alan Turing predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes. The Hungarian biologist Aristid Lindenmayer and the French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create plant growth patterns.

Mathematics, physics and chemistry can explain patterns in nature at different levels and scales. Patterns in living things are explained by the biological processes of natural selection and sexual selection. Studies of pattern formation make use of computer models to simulate a wide range of patterns.

History

Early Greek thinkers like Pythagoras and Plato tried to explain the order in nature. They believed that numbers and shapes were key to understanding the world around us.

Later, Leonardo Fibonacci introduced a special number pattern called the Fibonacci sequence, which appears in many plants. Scientists like Johannes Kepler and D'Arcy Wentworth Thompson studied how these patterns show up in flowers, shells, and more. In the 1900s, Alan Turing suggested that simple chemical reactions could create the spots and stripes we see in animals.

Causes

Living things like orchids, hummingbirds, and the peacock's tail show beautiful patterns that can be hard for artists to copy. These patterns come from many sources, including the math that rules how forms can appear and natural selection, which decides how patterns change over time.

Mathematics helps us understand these patterns through ideas like chaos theory, fractals, and spirals. The rules of physics also shape patterns in nature, like how meanders form in rivers. In biology, patterns help animals hide, attract mates, or warn others, like how insect-pollinated flowers have special shapes and colors to draw bees close.

Types of pattern

Symmetry

Further information: Symmetry in biology, Floral symmetry, and Crystal symmetry

Symmetry is common in living things. Animals usually have bilateral or mirror symmetry, like the leaves of plants and some flowers such as orchids. Plants often show radial or rotational symmetry, like many flowers and some animals such as sea anemones. Fivefold symmetry appears in echinoderms, including starfish, sea urchins, and sea lilies.

Non-living things also show symmetry. Snowflakes have striking sixfold symmetry, with each arm forming a similar pattern. Crystals have various symmetries, and rotational symmetry can be seen in patterns like the splash of a drop of water or the shape of planets such as Saturn.

Trees, fractals

The branching pattern of trees was described during the Italian Renaissance by Leonardo da Vinci. Trees split into branches in a way that balances their thickness. Fractals are patterns that repeat themselves at different scales. Examples in nature include the leaves of ferns and umbellifers, cloud shapes, river networks, and blood vessel branching.

Spirals

Further information: Phyllotaxis

Spirals are common in plants and some animals, like molluscs. In the nautilus, each chamber of the shell is a scaled copy of the next, arranged in a logarithmic spiral. Plant spirals appear in the arrangement of leaves on stems, in flower heads like the sunflower, and in pine cones. These spirals often follow Fibonacci ratios.

Chaos, flow, meanders

In nature, patterns can emerge from chaotic systems and fluid flow. Vortex streets are zigzag patterns created by fluid flow around obstacles. Meanders are the winding paths of rivers, formed by the movement of water and sediment over time.

Waves, dunes

Waves are energy-carrying disturbances that move through a medium. In nature, waves create patterns like ripples in sand and dunes in deserts. Dunes can form various shapes, such as crescents and long straight lines, depending on wind patterns.

Bubbles, foam

A soap bubble forms a sphere, the shape with the smallest surface area for its volume. Foam is a mass of bubbles, and natural foams follow certain rules, such as the angles at which bubble walls meet. Examples of natural foams include the skeletons of radiolarians and sponges.

Tessellations

Main article: Tessellation

Tessellations are patterns made by repeating shapes across a surface. Examples in nature include the cells of honeycomb made by bees and the scales on fish and snakes. Minerals also form repeating patterns in their crystal structures.

Cracks

Cracks form in materials to relieve stress. In elastic materials, cracks often meet at 120 degrees, while in inelastic materials, they form straight lines. The pattern of cracks can indicate the type of material and how it responds to stress.

Spots, stripes

Animals like leopards and ladybirds have spots, while others like angelfish and zebras have stripes. These patterns can help with camouflage or serve as warning signals to predators. For example, the bold colors of a ladybird can warn birds that it is bitter or poisonous.

Pattern formation

Main article: Pattern formation

Nature has many repeating patterns, like spots and stripes, that we see on animals and in landscapes. Scientists have found that these patterns can form through special chemical processes inside living things. For example, some cells can turn on and off based on chemicals called morphogens, creating spots or stripes on animal skin.

Patterns also appear in nature for other reasons. Plants can grow in stripes that collect rainwater, and forests can show wavy patterns after wind damage. Even the folds in our brains have patterns that form as the brain grows. These patterns show how nature uses simple rules to create beautiful and organized designs.