Patterns in nature

Patterns in nature are regular shapes and forms we see in the natural world. These patterns repeat in many places and can sometimes be described with math. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.

Early Greek philosophers like Plato, Pythagoras and Empedocles looked at patterns, trying to understand order in nature. Our knowledge of visible patterns grew slowly over time.

In the 1800s, a Belgian scientist named Joseph Plateau studied soap films and discovered ideas about minimal surfaces. A German biologist and artist, Ernst Haeckel, painted many marine organisms to show their symmetry. A Scottish biologist, D'Arcy Thompson, studied how plants and animals grow and found that simple math could explain spiral shapes.

In the 1900s, an English mathematician, Alan Turing, described how morphogenesis creates spots and stripes. A Hungarian biologist, Aristid Lindenmayer, and a French American mathematician, Benoît Mandelbrot, showed how fractals help explain plant growth.

Mathematics, physics and chemistry help us understand patterns in nature in many ways. Living things show patterns because of biological processes like natural selection. Scientists use computer models to study how many different patterns form.

History

Early Greek thinkers like Pythagoras and Plato tried to explain the order in nature. They thought numbers and shapes were important for understanding our world.

Later, Leonardo Fibonacci found a special number pattern called the Fibonacci sequence. This pattern appears in many plants. Scientists like Johannes Kepler and D'Arcy Wentworth Thompson looked at how these patterns appear in flowers, shells, and other things. In the 1900s, Alan Turing suggested that simple chemical reactions could create the spots and stripes we see on 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. They come from the math that rules how forms can appear and natural selection, which decides how patterns change over time.

Mathematics helps us understand these patterns. It uses 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. For example, 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 often have 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 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 sizes. 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 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. These patterns can form through special chemical processes inside living things. For example, some cells can change based on chemicals, creating spots or stripes on animal skin.

Patterns also appear in nature for other reasons. Plants can grow in stripes that help collect rainwater, and forests can show wavy patterns after wind. 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.