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 studied pattern, with Plato, Pythagoras and Empedocles attempting 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.
Introduction
Patterns in nature
Patterns in nature | Introduction
It includes symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. It include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.
what does patterns in nature refer to?
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They are visible regularities of form found in the natural world.
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what patterns does it include?
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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 studied pattern, with Plato, Pythagoras and Empedocles attempting 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.
Patterns in nature | Introduction
Natural patterns are sometimes formed by animals, as in the Mima mounds of the Northwestern United States and some other areas, which appear to be created over many years by the burrowing activities of pocket gophers, while the so-called fairy circles of Namibia appear to be created by the interaction of competing groups of sand termites, along with competition for water among the desert plants.
Patterns in nature | Pattern formation
Nature provides examples of many kinds of pattern, including symmetries, trees and other structures with a fractal dimension, spirals, meanders, waves, foams, tilings, cracks and stripes.
Pattern | Nature
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic, never exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection.
Pattern | Introduction
Living things like orchids, hummingbirds, and the peacock's tail have abstract designs with a beauty of form, pattern and colour that artists struggle to match. The beauty that people perceive in nature has causes at different levels, notably in the mathematics that governs what patterns can physically form, and among living things in the effects of natural selection, that govern how patterns evolve. Mathematics seeks to discover and explain abstract patterns or regularities of all kinds. Visual patterns in nature find explanations in chaos theory, fractals, logarithmic spirals, topology and other mathematical patterns. For example, L-systems form convincing models of different patterns of tree growth.
Patterns in nature | Causes
Pioneering authors General books Patterns from nature (as art)
Patterns in nature | Bibliography
The young leopards and ladybirds, inheriting genes that somehow create spottedness, survive. But while these evolutionary and functional arguments explain why these animals need their patterns, they do not explain how the patterns are formed.
Patterns in nature | Spots, stripes
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 British 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. 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.
Patterns in nature | Introduction
Apart from this nonlinearity, barchans behave rather like solitary waves.
Patterns in nature | Waves, dunes
Early Greek philosophers attempted to explain order in nature, anticipating modern concepts. Pythagoras (c. 570–c. 495 BC) explained patterns in nature like the harmonies of music as arising from number, which he took to be the basic constituent of existence. Empedocles (c. 494–c. 434 BC) to an extent anticipated Darwin's evolutionary explanation for the structures of organisms. Plato (c. 427–c. 347 BC) argued for the existence of natural universals. He considered these to consist of ideal forms ( "eidos": "form") of which physical objects are never more than imperfect copies. Thus, a flower may be roughly circular, but it is never a perfect circle.
Patterns in nature | History
One explanation is that this allows trees to better withstand high winds. Simulations of biomechanical models agree with the rule.
Patterns in nature | Trees, fractals
Since each species of tree has its own structure at the levels of cell and of molecules, each has its own pattern of splitting in its bark.
Patterns in nature | Cracks
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.
Patterns in nature | Chaos, flow, meanders
The laws of physics apply the abstractions of mathematics to the real world, often as if it were perfect. For example, a crystal is perfect when it has no structural defects such as dislocations and is fully symmetric. Exact mathematical perfection can only approximate real objects. Visible patterns in nature are governed by physical laws; for example, meanders can be explained using fluid dynamics.
Patterns in nature | Causes
Alan Turing, and later the mathematical biologist James Murray, described a mechanism that spontaneously creates spotted or striped patterns: a reaction–diffusion system. The cells of a young organism have genes that can be switched on by a chemical signal, a morphogen, resulting in the growth of a certain type of structure, say a darkly pigmented patch of skin. If the morphogen is present everywhere, the result is an even pigmentation, as in a black leopard. But if it is unevenly distributed, spots or stripes can result. Turing suggested that there could be feedback control of the production of the morphogen itself.
Patterns in nature | Pattern formation
Theophrastus (c. 372–c. 287 BC) noted that plants "that have flat leaves have them in a regular series"; Pliny the Elder (23–79 AD) noted their patterned circular arrangement. Centuries later, Leonardo da Vinci (1452–1519) noted the spiral arrangement of leaf patterns, that tree trunks gain successive rings as they age, and proposed a rule purportedly satisfied by the cross-sectional areas of tree-branches. Johannes Kepler (1571–1630) pointed out the presence of the Fibonacci sequence in nature, using it to explain the pentagonal form of some flowers. In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series.
Patterns in nature | History
Tessellations are patterns formed by repeating tiles all over a flat surface. There are 17 wallpaper groups of tilings. While common in art and design, exactly repeating tilings are less easy to find in living things. The cells in the paper nests of social wasps, and the wax cells in honeycomb built by honey bees are well-known examples. Among animals, bony fish, reptiles or the pangolin, or fruits like the salak are protected by overlapping scales or osteoderms, these form more-or-less exactly repeating units, though often the scales in fact vary continuously in size. Among flowers, the snake's head fritillary, "Fritillaria meleagris", have a tessellated chequerboard pattern on their petals.
Patterns in nature | Tessellations
Some mathematical rule-patterns can be visualised, and among these are those that explain patterns in nature including the mathematics of symmetry, waves, meanders, and fractals. Fractals are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their formation can be simple (e.g. Lindenmayer systems describing tree shapes).
Pattern | Fractals
Chaos theory predicts that while the laws of physics are deterministic, there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes.. The patterns in nature tend to be static due to dissipation on the emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic. Many natural patterns are shaped by this complexity, including vortex streets, other effects of turbulent flow such as meanders in rivers. or nonlinear interaction of the system
Pattern | Chaos, turbulence, meanders and complexity
Patterns can form for other reasons in the vegetated landscape of tiger bush and fir waves. Tiger bush stripes occur on arid slopes where plant growth is limited by rainfall. Each roughly horizontal stripe of vegetation effectively collects the rainwater from the bare zone immediately above it. Fir waves occur in forests on mountain slopes after wind disturbance, during regeneration. When trees fall, the trees that they had sheltered become exposed and are in turn more likely to be damaged, so gaps tend to expand downwind. Meanwhile, on the windward side, young trees grow, protected by the wind shadow of the remaining tall trees.
Patterns in nature | Pattern formation
This could cause continuous fluctuations in the amount of morphogen as it diffused around the body. A second mechanism is needed to create standing wave patterns (to result in spots or stripes): an inhibitor chemical that switches off production of the morphogen, and that itself diffuses through the body more quickly than the morphogen, resulting in an activator-inhibitor scheme. The Belousov–Zhabotinsky reaction is a non-biological example of this kind of scheme, a chemical oscillator. Later research has managed to create convincing models of patterns as diverse as zebra stripes, giraffe blotches, jaguar spots (medium-dark patches surrounded by dark broken rings) and ladybird shell patterns (different geometrical layouts of spots and stripes, see illustrations).
Patterns in nature | Pattern formation
A result of this formula is that any closed polyhedron of hexagons has to include exactly 12 pentagons, like a soccer ball, Buckminster Fuller geodesic dome, or fullerene molecule. This can be visualised by noting that a mesh of hexagons is flat like a sheet of chicken wire, but each pentagon that is added forces the mesh to bend (there are fewer corners, so the mesh is pulled in).
Patterns in nature | Bubbles, foam
More puzzling is the reason for the fivefold (pentaradiate) symmetry of the echinoderms. Early echinoderms were bilaterally symmetrical, as their larvae still are. Sumrall and Wray argue that the loss of the old symmetry had both developmental and ecological causes.
Patterns in nature | Symmetry
No better solution was found until 1993 when Denis Weaire and Robert Phelan proposed the Weaire–Phelan structure; the Beijing National Aquatics Center adapted the structure for their outer wall in the 2008 Summer Olympics. At the scale of living cells, foam patterns are common; radiolarians, sponge spicules, silicoflagellate exoskeletons and the calcite skeleton of a sea urchin, "Cidaris rugosa", all resemble mineral casts of Plateau foam boundaries. The skeleton of the Radiolarian, "Aulonia hexagona", a beautiful marine form drawn by Ernst Haeckel, looks as if it is a sphere composed wholly of hexagons, but this is mathematically impossible. The Euler characteristic states that for any convex polyhedron, the number of faces plus the number of vertices (corners) equals the number of edges plus two.
Patterns in nature | Bubbles, foam
The distinction between spatial and spatio-temporal patterns in nature is not clear-cut because a static, invariable pattern will never occur in the strict sense. Even rock formations will slowly change on a time-scale of 10s of millions of years, therefore the distinction lies in the time scale of change in relation to human experience. Already the snapshot state of a dune will usually be taken as an example of a purely spatial pattern although this is clearly not the case. It is thus apt to say that spatiotemporal patterns in nature are the rule rather than the exception.
Spatiotemporal pattern | Exception or rule?
In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book "Liber Abaci". Fibonacci presented a thought experiment on the growth of an idealized rabbit population.
Patterns in nature | History
Fractal curves and fractal patterns are widespread, in nature, found in such places as broccoli, snowflakes, feet of geckos, frost crystals, and lightning bolts. See also Romanesco broccoli, dendrite crystal, trees, fractals, Hofstadter's butterfly, Lichtenberg figure, and self-organized criticality.
Fractal curve | Fractal curves in nature
Spatial patterns, such as the distribution of a species, are the result of either true or induced spatial autocorrelation. In nature, organisms are distributed neither uniformly nor at random. The environment is spatially structured by various ecological processes, which in combination with the behavioral response of species’ generally results in: Theoretically, any of these structures may occur at any given scale. Due to the presence of spatial autocorrelation, in nature gradients are generally found at the global level, whereas patches represent intermediate (regional) scales, and noise at local scales. The analysis of spatial ecological patterns comprises two families of methods;
Spatial ecology | Pattern
Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world. In art and architecture, decorations or visual motifs may be combined and repeated to form patterns designed to have a chosen effect on the viewer. In computer science, a software design pattern is a known solution to a class of problems in programming. In fashion, the pattern is a template used to create any number of similar garments.
Pattern | Introduction
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.
Patterns in nature | Chaos, flow, meanders
The structures of minerals provide good examples of regularly repeating three-dimensional arrays. Despite the hundreds of thousands of known minerals, there are rather few possible types of arrangement of atoms in a crystal, defined by crystal structure, crystal system, and point group; for example, there are exactly 14 Bravais lattices for the 7 lattice systems in three-dimensional space.
Patterns in nature | Tessellations
Leopards and ladybirds are spotted; angelfish and zebras are striped. These patterns have an evolutionary explanation: they have functions which increase the chances that the offspring of the patterned animal will survive to reproduce. One function of animal patterns is camouflage; for instance, a leopard that is harder to see catches more prey. Another function is signalling — for instance, a ladybird is less likely to be attacked by predatory birds that hunt by sight, if it has bold warning colours, and is also distastefully bitter or poisonous, or mimics other distasteful insects. A young bird may see a warning patterned insect like a ladybird and try to eat it, but it will only do this once; very soon it will spit out the bitter insect; the other ladybirds in the area will remain undisturbed.
Patterns in nature | Spots, stripes
Cracks are linear openings that form in materials to relieve stress. When an elastic material stretches or shrinks uniformly, it eventually reaches its breaking strength and then fails suddenly in all directions, creating cracks with 120 degree joints, so three cracks meet at a node. Conversely, when an inelastic material fails, straight cracks form to relieve the stress. Further stress in the same direction would then simply open the existing cracks; stress at right angles can create new cracks, at 90 degrees to the old ones. Thus the pattern of cracks indicates whether the material is elastic or not. In a tough fibrous material like oak tree bark, cracks form to relieve stress as usual, but they do not grow long as their growth is interrupted by bundles of strong elastic fibres.
Patterns in nature | Cracks
These arrangements have explanations at different levels – mathematics, physics, chemistry, biology – each individually correct, but all necessary together. Phyllotaxis spirals can be generated mathematically 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. In disc phyllotaxis as in the sunflower and daisy, the florets are arranged in Fermat's spiral with Fibonacci numbering, at least when the flowerhead is mature so all the elements are the same size.
Patterns in nature | Spirals
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.
Patterns in nature | Waves, dunes
In 2017 Corina Tarnita and colleagues published a paper in "Nature" which explained these and other related self-organised vegetation patterns by means of a general theory which integrates scale-dependent feedbacks and the activities of subterranean ecosystem engineers such as termites, ants, and rodents.
Heuweltjie | Nature Paper explanation
A pattern is an original object used to make copies, or a set of repeating objects in a decorative design and in other disciplines. Pattern, patterns, or patterning may also refer to:
Pattern (disambiguation) | Introduction
Alan Turing, and later the mathematical biologist James D. Murray and other scientists, described a mechanism that spontaneously creates spotted or striped patterns, for example in the skin of mammals or the plumage of birds: a reaction–diffusion system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin. These spatiotemporal patterns slowly drift, the animals' appearance changing imperceptibly as Turing predicted.
Pattern | Spots, stripes
Mathematical observations of phyllotaxis followed with Karl Friedrich Schimper and his friend Alexander Braun's 1830 and 1830 work, respectively; Auguste Bravais and his brother Louis connected phyllotaxis ratios to the Fibonacci sequence in 1837, also noting its appearance in pinecones and pineapples. In his 1854 book, German psychologist Adolf Zeising explored the golden ratio expressed in the arrangement of plant parts, the skeletons of animals and the branching patterns of their veins and nerves, as well as in crystals. A. H. Church studied the patterns of phyllotaxis in his 1904 book. In 1917, D'Arcy Thompson published "On Growth and Form"; his description of phyllotaxis and the Fibonacci sequence, the mathematical relationships in the spiral growth patterns of plants showed that simple equations could describe the spiral growth patterns of animal horns and mollusc shells.
Patterns in nature | History
The branching pattern of trees was described in the Italian Renaissance by Leonardo da Vinci. He stated that: All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk [below them]. A more general version states that when a parent branch splits into two or more child branches, the surface areas of the child branches add up to that of the parent branch. An equivalent formulation is that if a parent branch splits into two child branches, then the cross-sectional diameters of the parent and the two child branches form a right-angled triangle.
Patterns in nature | Trees, fractals
Examples of pattern formation can be found in biology, chemistry, physics, and mathematics, and can readily be simulated with computer graphics, as described in turn below.
Pattern formation | Examples
Richard Prum's activation-inhibition models, developed from Turing's work, use six variables to account for the observed range of nine basic within-feather pigmentation patterns, from the simplest, a central pigment patch, via concentric patches, bars, chevrons, eye spot, pair of central spots, rows of paired spots and an array of dots. More elaborate models simulate complex feather patterns in the guineafowl "Numida meleagris" in which the individual feathers feature transitions from bars at the base to an array of dots at the far (distal) end. These require an oscillation created by two inhibiting signals, with interactions in both space and time.
Patterns in nature | Pattern formation
Although some species show variations in pattern, many species can be recognized on the basis of the patterns.
Gergithus | Introduction
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.
Patterns in nature | Waves, dunes
This pattern does not seem to follow any particular climatic rule and may be due to other environmental factors, such as predation and human encroachment.
Platypus | Description
Symmetry is pervasive in living things. Animals mainly have bilateral or mirror symmetry, as do the leaves of plants and some flowers such as orchids. Plants often have radial or rotational symmetry, as do many flowers and some groups of animals such as sea anemones. Fivefold symmetry is found in the echinoderms, the group that includes starfish, sea urchins, and sea lilies. Among non-living things, snowflakes have striking sixfold symmetry; each flake's structure forms a record of the varying conditions during its crystallization, with nearly the same pattern of growth on each of its six arms. Crystals in general have a variety of symmetries and crystal habits; they can be cubic or octahedral, but true crystals cannot have fivefold symmetry (unlike quasicrystals).
Patterns in nature | Symmetry
Constraints which produce emergent phenomena may not be a process which can be understood by looking at the make-up of the constituents of a pattern. Emergent phenomena are difficult to study because their complexity does not necessarily decompose into parts. When a pattern is broken down, the constraints are no longer at work; there is no hole, no absence to notice. Imagine a hub, a hole for an axle, produced only when the wheel is rolling, thus breaking the wheel may not show you how the hub emerges.
Incomplete Nature | Constraints
For natural occurrences of regular polyhedra, see . Irregular polyhedra appear in nature as crystals.
Polyhedron | In nature
The presence of a clear directionality to some important factor (such as a freezing wind or surface flow down a slope) favors the formation of stripes (bands), oriented perpendicular to the flow direction, in wider ranges of rainfall rates. Several mathematical models have been published that reproduce a wide variety of patterned landscapes, including: hexagonal “fairy-circle” gap patterns, woody-herbaceous landscapes, salt marshes, Although not strictly vegetation, sessile marine invertebrates such as mussels and oysters, have also been shown to form banding patterns.
Patterned vegetation | Introduction
On large scales, the pattern of distribution among individuals in a population is clumped. On small scales, the pattern may be clumped, regular, or random.
Species distribution | Patterns on small scales
Further, as Cuthill and Székely indicate, the bodies of animals that have such patterns must therefore have been shaped by natural selection.
Coincident disruptive coloration | Evidence for natural selection
Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed.
Pattern formation | Mathematics
A soap bubble forms a sphere, a surface with minimal area — the smallest possible surface area for the volume enclosed. Two bubbles together form a more complex shape: the outer surfaces of both bubbles are spherical; these surfaces are joined by a third spherical surface as the smaller bubble bulges slightly into the larger one. A foam is a mass of bubbles; foams of different materials occur in nature. Foams composed of soap films obey Plateau's laws, which require three soap films to meet at each edge at 120° and four soap edges to meet at each vertex at the tetrahedral angle of about 109.5°.
Patterns in nature | Bubbles, foam
In flat terrains additional pattern morphologies appear besides stripes - hexagonal gap patterns and hexagonal spot patterns. Pattern formation in this case is driven by positive feedback loops between local vegetation growth and water transport towards the growth location.
Pattern formation | Vegetation patterns
These patterns in the vegetation can appear without any underlying pattern in soil types, and are thus said to “self-organize” rather than be determined by the environment. Several of the mechanisms underlying patterning of vegetation have been known and studied since at least the middle of the 20th century, however, mathematical models replicating them have only been produced much more recently. Self-organization in spatial patterns is often a result of spatially uniform states becoming unstable through the monotonic growth and amplification of nonuniform perturbations. A well known instability of this kind leads to so-called Turing patterns. These patterns occur at many scales of life, from cellular development (where they were first proposed) to pattern formation on animal pelts to sand dunes and patterned landscapes (see also pattern formation).
Patterned vegetation | Introduction
Rotational symmetry is found at different scales among non-living things, including the crown-shaped splash pattern formed when a drop falls into a pond, and both the spheroidal shape and rings of a planet like Saturn. Symmetry has a variety of causes. Radial symmetry suits organisms like sea anemones whose adults do not move: food and threats may arrive from any direction. But animals that move in one direction necessarily have upper and lower sides, head and tail ends, and therefore a left and a right. The head becomes specialised with a mouth and sense organs (cephalisation), and the body becomes bilaterally symmetric (though internal organs need not be).
Patterns in nature | Symmetry
In their simplest form models that capture Turing instabilities require two interactions at differing scales: local facilitation and more distant competition. For example, when Sato and Iwasa produced a simple model of fir waves in the Japanese Alps, they assumed that trees exposed to cold winds would suffer mortality from frost damage, but upwind trees would protect nearby downwind trees from wind. Banding appears because the protective boundary layer created by the wind-most trees is eventually disrupted by turbulence, exposing more distant downwind trees to freezing damage once again. When there is no directional resource flow across the landscape, spatial patterns may still appear in various regular and irregular forms along the rainfall gradient, including, in particular, hexagonal gap patterns at relatively high rainfall rates, stripe patterns at intermediate rates, and hexagonal spot patterns at low rates.
Patterned vegetation | Introduction
Among them may be cited :
Le Tallec's patterns | Introduction
The English mathematician Alan Turing introduced a concept, which came to be known as a Turing pattern, in a 1952 paper entitled "The Chemical Basis of Morphogenesis". This foundational paper describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. In his classic paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Turing hypothesized that the resulting wavelike patterns are the chemical basis of morphogenesis.
Turing pattern | Introduction
On large scales, the pattern of distribution among individuals in a population is clumped.
Species distribution | Patterns on large scales
Plateau's laws further require films to be smooth and continuous, and to have a constant average curvature at every point. For example, a film may remain nearly flat on average by being curved up in one direction (say, left to right) while being curved downwards in another direction (say, front to back). Structures with minimal surfaces can be used as tents. Lord Kelvin identified the problem of the most efficient way to pack cells of equal volume as a foam in 1887; his solution uses just one solid, the bitruncated cubic honeycomb with very slightly curved faces to meet Plateau's laws.
Patterns in nature | Bubbles, foam
This pattern of patches is assumed by other species at night, but only "N. espei" displays the pattern permanently and in daylight.
Nannostomus espei | Introduction
Greig-Smith was fascinated by the phenomenon of plant spatial pattern, defined by the question: why are some plants regularly spaced while others are densely clumped? He realized that plants could be clumped at a certain scale, but that those clumps, in turn, could be randomly, or even regularly distributed at larger scales. Patterns and processes in ecology, he concluded, can have different behaviors at different scale. Strongly influenced by his early experience in agricultural experiments using random blocks and nested designs, he sought to answer this question by using, as his core tool, a series of quadrats nested within each other at different scales.
Peter Greig-Smith | Pattern and Scaling in Ecological Sciences
Foams obey Plateau's laws, which require films to be smooth and continuous, and to have a constant average curvature. Foam and bubble patterns occur widely in nature, for example in radiolarians, sponge spicules, and the skeletons of silicoflagellates and sea urchins.
Pattern | Bubbles, foam
The attitude and very striking colour-scheme thus combine to produce an extraordinary effect, whose deceptive appearance depends upon the breaking up of the entire form into two strongly contrasted areas of brown and white. Considered separately, neither part resembles part of a frog. Together in nature the white configuration alone is conspicuous. This stands out and distracts the observer's attention from the true form and contour of the body and appendages on which it is superimposed". Cott concluded that the effect was concealment "so long as the false configuration is recognized in preference to the real one". Such patterns embody, as Cott stressed, considerable precision as the markings must line up accurately for the disguise to work.
Coloration evidence for natural selection | Coincident disruptive coloration
In pattern theory, devised by Ulf Grenander, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner. In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns.
Pattern | Fractals
Fibonacci ratios approximate the golden angle, 137.508°, which governs the curvature of Fermat's spiral. 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.
Patterns in nature | Spirals
Numbers in Nature: A Mirror Maze contains an interactive theater and stations to learn about patterns in nature, including the Golden Ratio, spirals, fractal branching, and Voronoi patterns. It also contains a mirror maze to help emphasize the geometric patterns that can be utilized.
Museum of Science and Industry (Chicago) | Numbers in Nature: A Mirror Maze
Patterned vegetation is a vegetation community that exhibits distinctive and repetitive patterns. Examples of patterned vegetation include fir waves, tiger bush, and string bog. The patterns typically arise from an interplay of phenomena that differentially encourage plant growth or mortality. A coherent pattern arises because there is a strong directional component to these phenomena, such as wind in the case of fir waves, or surface runoff in the case of tiger bush. The regular patterning of some types of vegetation is a striking feature of some landscapes. Patterns can include relatively evenly spaced patches, parallel bands or some intermediate between those two.
Patterned vegetation | Introduction
The two patterns are also unofficially known as "Lowland" and "Highland" ERDL, respectively.
ERDL pattern | Introduction
These shape of cloud patterns were different by era. Each pattern reflected different social backgrounds.
Traditional patterns of Korea | Natural (Landscape) pattern
Cracks form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics.
Pattern | Cracks
The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. Pattern formation is controlled by genes. The role of genes in pattern formation is an aspect of morphogenesis, the creation of diverse anatomies from similar genes, now being explored in the science of evolutionary developmental biology or evo-devo. The mechanisms involved are well seen in the anterior-posterior patterning of embryos from the model organism "Drosophila melanogaster" (a fruit fly), one of the first organisms to have its morphogenesis studied and in the eyespots of butterflies, whose development is a variant of the standard (fruit fly) mechanism.
Pattern formation | Introduction
Nature patterns are patterns that use things found in nature, excluding animals and plants. Common themes are: Sun, moon, and stars. Landscapes and strangely shaped rocks are also common. These patterns usually symbolize longevity, because of their immutability. Cloud is the most common nature pattern. In the past, people believed if they pursued for virtue while they lived, they could rise to sky riding a cloud or attain Buddha-hood. Cloud patterns are also used to represent dragon's divine spirit. Patterns with cranes are usually also seen with clouds in the background. Cloud patterns are divided into three shapes. The first shape is clouds being blown in the wind, the second shape is clouds floating in the sky, and the third is scattered and dotted clouds.
Traditional patterns of Korea | Natural (Landscape) pattern
Each loop on the pattern is called a cormidium.
Physonectae | Introduction
Many patterns seen in nature are closely approximated by a centroidal Voronoi tessellation. Examples of this include the Giant's Causeway, the cells of the cornea, and the breeding pits of the male tilapia.
Centroidal Voronoi tessellation | Occurrence in nature
This creates patterns with two colors.
Damaskeening | Introduction
Existing patterns of biodiversity have been shaped by repeated formations of new species (speciation), changes within species (anagenesis) and loss of species (extinction) throughout the evolutionary history of life on Earth. Morphological and biochemical traits are more similar among species that share a more recent common ancestor, and can be used to reconstruct phylogenetic trees.
Evolution | Introduction
Spiral patterns are found in the body plans of animals including molluscs such as the nautilus, and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple.
Pattern | Spirals
A pattern is a discernible regularity in the world or in a manmade design. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeating like a wallpaper. A relation on a set "A" is a collection of ordered pairs of elements of "A". In other words, it is a subset of the Cartesian product "A" = . Common relations include divisibility between two numbers and inequalities. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Elementary mathematics | Patterns, relations and functions
These patterns are variable even within populations, including the bands curving or breaking into discontinuous lines or spots.
Hyperolius swynnertoni | Description
Chapter four explains the schema of the "three natures" ("trisvabhāva"): the imagined, the other-dependent and the fully perfected. These are described as follows:The pattern of clinging to what is entirely imagined refers to the establishing of names and symbols for all things and the distinguishing of their essences, whereby they come to be expressed in language. The pattern of other-dependency refers to the pattern whereby all things arise co-dependently: for if this exists, then that exists, and if this arises, then that arises. This refers to [the twelvefold conditions, starting with] 'conditioned by ignorance are karmic formations,' [and ending with] 'conditioned by origination is this grand mass of suffering,' [the last of the twelve conditions].
Sandhinirmocana Sutra | Chapter 4: The Characteristic Patterns of All Things
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.
Patterns in nature | Spirals
Some more images of patterns in bacterial growth can be found in:
Bacterial patterns | External links
However, a sufficient explanation for this observable pattern has yet to be produced.
Temperature-size rule | Reproduction
Ramsey's next argumentative manoeuvre is to point out that traits are not randomly scattered across potential life histories; there are patterns. “These patterns” he states “provide the basis for the notion of individual and human nature”. While one's ‘individual nature’ consists of the pattern of trait clusters distributed across that individual's set of possible life histories, Human Nature, Ramsey defines as “the pattern of trait clusters within the totality of extant human possible life histories”. Thus, if we were to combine all possible life histories of all individuals in existence we would have access to the trait distribution patterns that constitute human nature.
Human nature | "Life-history trait cluster" account (Ramsey)
Nature, in the broadest sense, is the natural, physical, or material world or universe. Nature may also refer to:
Nature (disambiguation) | Introduction
In 2017, Corina Tarnita and several of her colleagues published a paper in "Nature" which explained these and other related self-organised vegetation patterns by means of a general theory which integrates scale-dependent feedbacks and the activities of subterranean ecosystem engineers such as termites, ants, and rodents.
Mima mounds | Nature Paper explanation
Whereas scholars and theologians once held a symbolist mentality of the natural world as expressive of spiritual realities, intellectual thinking now regarded nature as a “coherent entity which could be systematically investigated by the senses. The idea of nature is that of a particular ordering of natural objects, and the study of nature the systematic investigation of that order.” The notion of order in nature implied a structure to the physical world whereby relationships between objects could be defined. According to Harrison, the twelfth century marked an important time in the Christian era when the world became invested with its own patterns of order—patterns based on networks of likeness or similarities among material things, which served to determine the character of a pre-modern knowledge of nature.
Book of Nature | Rediscovering the natural world
Some examples of creational design patterns include:
Creational pattern | Examples
In the wet season, mate selection returned to 1:1 proportions.
Anartia fatima | Genetics of color patterns
Below is a simple class diagram that most creational patterns have in common. Note that different creational patterns require additional and different participated classes. Participants:
Creational pattern | Structure
Water and light give movement to the patterns.
Kabinettsgarten | Layout
Embryos develop inside the female, and the life cycle repeats.
Acanthocephala | General patterns
The series of patterns is as follows:
Gutmann method | Method
The resulting pattern of yardangs is therefore a combination of the original rock distribution, and the fluid mechanics of the air flow and resulting pattern of erosion.
Yardang | Introduction
A mimetolithic pattern is a pattern created by rocks that may come to mimic recognizable forms through the random processes of formation, weathering and erosion. Picture jaspers exhibit combinations of patterns such as banding from flow or depositional patterns (from water or wind), or dendritic or color variations, resulting in what appear to be miniature scenes on a cut section, which is then used for jewelry. More often, the size scale of the rock is larger than the object it resembles, such as a cliff profile resembling a human face. Well-meaning people with a new interest in fossils can pick up chert nodules, concretions or pebbles resembling bones, skulls, turtle shells, dinosaur eggs, etc., in both size and shape.
Pareidolia | Mimetoliths
Comparisons between the scleral rings of "Archaeopteryx" and modern birds and reptiles indicate that it may have been diurnal, similar to most modern birds.
Archaeopteryx | Daily activity patterns
Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.
Pattern | Science and mathematics
Several qualitative observations can be made of diffraction in general:
Diffraction | Patterns