---
title: "Patterns in nature"
chunk: 3/5
source: "https://en.wikipedia.org/wiki/Patterns_in_nature"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:40:02.241373+00:00"
instance: "kb-cron"
---

Spirals are common in plants and in some animals, notably molluscs. For example, in the nautilus, a cephalopod mollusc, each chamber of its shell is an approximate copy of the next one, scaled by a constant factor and arranged in a logarithmic spiral. Given a modern understanding of fractals, a growth spiral can be seen as a special case of self-similarity.
Plant spirals can be seen in phyllotaxis, the arrangement of leaves on a stem, and in the arrangement (parastichy) of other parts as in composite flower heads and seed heads like the sunflower or fruit structures like the pineapple and snake fruit, as well as in the pattern of scales in pine cones, where multiple spirals run both clockwise and anticlockwise. These arrangements have explanations at different levels – mathematics, physics, chemistry, biology – each individually correct, but all necessary together. Phyllotaxis spirals can be generated from Fibonacci ratios: the Fibonacci sequence runs 1, 1, 2, 3, 5, 8, 13... (each subsequent number being the sum of the two preceding ones). For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is 1/3; in apricot it is 2/5; in pear it is 3/8; in almond it is 5/13.  Animal behaviour can yield spirals; for example, acorn worms leave spiral fecal trails on the sea floor. 
In disc phyllotaxis as in the sunflower and daisy, the florets are arranged along Fermat's spiral, but this is disguised because successive florets are spaced far apart, by the golden angle, 137.508° (dividing the circle in the golden ratio); when the flowerhead is mature so all the elements are the same size, this spacing creates a Fibonacci number of more obvious spirals.
From the point of view of physics, spirals are lowest-energy configurations which emerge spontaneously through self-organizing processes in dynamic systems. From the point of view of chemistry, a spiral can be generated by a reaction-diffusion process, involving both activation and inhibition. Phyllotaxis is controlled by proteins that manipulate the concentration of the plant hormone auxin, which activates meristem growth, alongside other mechanisms to control the relative angle of buds around the stem. From a biological perspective, arranging leaves as far apart as possible in any given space is favoured by natural selection as it maximises access to resources, especially sunlight for photosynthesis.

=== Chaos, flow, meanders ===
In mathematics, a dynamical system is chaotic if it is (highly) sensitive to initial conditions (the so-called "butterfly effect"), which requires the mathematical properties of topological mixing and dense periodic orbits.
Alongside fractals, chaos theory ranks as an essentially universal influence on patterns in nature. There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. Some cellular automata, simple sets of mathematical rules that generate patterns, have chaotic behaviour, notably Stephen Wolfram's Rule 30.
Vortex streets are zigzagging patterns of whirling vortices created by the unsteady separation of flow of a fluid, most often air or water, over obstructing objects. Smooth (laminar) flow starts to break up when the size of the obstruction or the velocity of the flow become large enough compared to the viscosity of the fluid.
Meanders are sinuous bends in rivers or other channels, which form as a fluid, most often water, flows around bends. As soon as the path is slightly curved, the size and curvature of each loop increases as helical flow drags material like sand and gravel across the river to the inside of the bend. The outside of the loop is left clean and unprotected, so erosion accelerates, further increasing the meandering in a powerful positive feedback loop.

=== Waves, dunes ===
Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by. Wind waves are sea surface waves that create the characteristic chaotic pattern of any large body of water, though their statistical behaviour can be predicted with wind wave models. As waves in water or wind pass over sand, they create patterns of ripples. When winds blow over large bodies of sand, they create dunes, sometimes in extensive dune fields as in the Taklamakan desert. Dunes may form a range of patterns including crescents, very long straight lines, stars, domes, parabolas, and longitudinal or seif ("sword") shapes.
Barchans or crescent dunes are produced by wind acting on desert sand; the two horns of the crescent and the slip face point downwind. Sand blows over the upwind face, which stands at about 15 degrees from the horizontal, and falls onto the slip face, where it accumulates up to the angle of repose of the sand, which is about 35 degrees. When the slip face exceeds the angle of repose, the sand avalanches, which is a nonlinear behaviour: the addition of many small amounts of sand causes nothing much to happen, but then the addition of a further small amount suddenly causes a large amount to avalanche. Apart from this nonlinearity, barchans behave rather like solitary waves.