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.
Causes
Patterns in nature
Patterns in nature | Causes
Causes can be 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. Sorry. I cannot find the answer based on the context. The mathematics that governs what patterns can physically form, and among living things in the effects of natural selection, that govern how patterns evolve. Chaos theory, fractals, logarithmic spirals, topology and other mathematical patterns.
what does patterns in nature refer to?
user
They are visible regularities of form found in the natural world.
assistant
what patterns does it include?
user
It includes symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.
assistant
what is it caused by?
user
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
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
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
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
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
The honeycomb is a well-known example of tessellation in nature with its hexagonal cells. In botany, the term "tessellate" describes a checkered pattern, for example on a flower petal, tree bark, or fruit. Flowers including the fritillary and some species of "Colchicum" are characteristically tessellate. Many patterns in nature are formed by cracks in sheets of materials. These patterns can be described by Gilbert tessellations, also known as random crack networks. The Gilbert tessellation is a mathematical model for the formation of mudcracks, needle-like crystals, and similar structures. The model, named after Edgar Gilbert, allows cracks to form starting from randomly scattered over the plane; each crack propagates in two opposite directions along a line through the initiation point, its slope chosen at random, creating a tessellation of irregular convex polygons.
Tessellation | In nature
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
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
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
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
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
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
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
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
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
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
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
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
Patterned by Nature was commissioned by the North Carolina Museum of Natural Sciences in Raleigh, North Carolina. This piece was a collaboration between Hypersonic, Sosolimited, and Plebian Design. 10 feet wide and 90 feet in length, this sculptural ribbon winds through a five story atrium of the newly built Nature Research Center museum expansion. "The exhibit celebrates the abstraction of nature's infinite complexity into patterns through the scientific process. It brings to light the similarity of patterns in our universe, across all scales of space and time.", says Bill Washabaugh, one of the project designers. The ribbon is made of 3,600 tiles of individually dimmable LCD glass, and runs on a total of about 75 watts of power.
Patterned by Nature | Introduction
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
The cause of this phenomenon is currently under debate; the most likely connection is with the mathematical theory of chaos and may give insights into the way patterns in sand form.
Oscillon | Introduction
Apart from this nonlinearity, barchans behave rather like solitary waves.
Patterns in nature | Waves, dunes
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
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
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
Pioneering authors General books Patterns from nature (as art)
Patterns in nature | Bibliography
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
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
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
Such rippled patterns result from increased cell growth near the edges of the leaf, which causes its thin, planar surface to buckle as it assumes the conformation with the lowest energy state.
Nepenthes maxima | Variability
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
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
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
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
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
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
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
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
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
If this falling process is not symmetrical on either side, then there will be a double parallel ribbon shape form, whereas a symmetrical fall will produce only a single parallel ribbon. A sporadic or insufficient fall of filamentary material will cause bright knots of solar flares to be produced.
Hyder flare | Cause
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 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?
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
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
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
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
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
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
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
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
In the spring, various shapes appear because frost is disappearing from the surface, exposing the underling dark soil. Also, in some places dust is blown out of in geyser-like eruptions that are sometimes called "spiders." If a wind is blowing, the material creates a long, dark streak or fan.
Vastitas Borealis | Defrosting
The impulse is reflected back from the end of the basin, generating interference. Repeated reflections produce standing waves with one or more nodes, or points, that experience no vertical motion. The frequency of the oscillation is determined by the size of the basin, its depth and contours, and the water temperature.
Seiche | Causes and nature
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 form by constant wetting and drying of the heavy clay soils.
Southwood National Park | Introduction
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
Instead of pigments, the colors are caused by the interference, diffraction, or scattering of light by numerous tiny structures. In "Poecilocoris lewisi", multiple tiny conical protuberances around 900 nm in height and averaging at a diameter of 360 nm are scattered on the epicuticle. These structures affect light passing through them, producing their oily-looking blue sheen (known as the Tyndall effect or Mie scattering).
Scutelleridae | Colors
They become noticeable at a diameter of about , achieving a peak diameter of perhaps , after which they mature and "die" as they undergo invasion, mainly by grasses. Like the heuweltjies and Mima mounds, the cause of fairy circles has long been a puzzle and the investigation has proved challenging. One favoured theory is that the distinct vegetation patterns are a population-level consequence of competition for scarce water, as the plants "organise" themselves to maximise access to scarce resources. The circular barren patches capture water which then flows to the outer edges of the ring. More water available increases biomass and roots which leads to the soil becoming looser.
Fairy circle (arid grass formation) | Introduction
"“I'm currently building structures as parallels to patterns of natural occurrences. My work examines the subtle movements around us, and the patterns those movements create. I am trying to compare the cyclical patterns found in nature with manufactured objects, environments, and modes of transportation."" ~Brose Partington, 2009 Partington's father owned a clock repair shop in Indianapolis during his childhood. The clocks, gears, and mechanisms of his father's shop influence his sculptures today. Most of his current work is kinetic with references to the patterns of nature. "Tides", a work shown internationally, is an example of the relationship between nature and machine found throughout Partington’s installations.
Entangled (Partington) | Artist statement
The strong aggregated patterning is thought to be the result of several non-exclusive processes. First, by creating the initial template on which post-dispersal processes act, its seed dispersers like foxes and badgers can be partially responsible for "P. bourgaena" aggregation. Second, dispersal limitation sometimes leads to seedling establishment beneath mother trees, resulting in an aggregated patterning. This is a likely possibility since a fraction of the fruit fallen beneath adult trees are not taken by mammals or are partially depulped by rabbits, without dispersing the seeds. Some seedlings emerge beneath mother trees every season and,eventually, a few of them get established.
Pyrus bourgaeana | Phenology and interactions with animals
Jagged patterns within result from interactions with interstellar wind, radiation pressure, magnetic fields, and gravity.
DR 21 | Introduction
Syrtis Major was the object of much observation due to its seasonal and long-term variations. This led to theories that it was a shallow sea and later that its variability was due to seasonal vegetation. However, in the 1960s and 1970s, the Mariner and Viking planetary probes led scientists to conclude that the variations were caused by wind blowing dust and sand across the area. It has many windblown deposits that include light-colored halos or "plumose streaks" that form downwind of craters. These streaks are accumulations of dust resulting from disruption of the wind by the elevated rims of the craters ('wind shadows').
Syrtis Major Planum | Seasonal variations
It is not yet clear what caused boulders to form patterns, but it does not seem that fractures caused the boulders to move around.
Polygonal patterned ground | Introduction
The sea exhibits complex spatial patterning that can be mapped and quantified, such as gradients in plant communities across tidal saltmarshes or the intricate mosaics of patches typical of coral reefs. In the open ocean too, dynamic spatial structure in the form of water currents, eddies, temperature fronts and plankton patches can be measured readily. Physical processes such as storms dramatically influence spatial patterning in the environment and human activity can also directly create patch structure, modify mosaic composition and even completely remove elements of the seascape. Furthermore, climate-change induced shifts in species related to water temperature change and sea level rise are driving a gradual reconfiguration of the geography of species and habitats.
Seascape ecology | Seascape patterns
These patterns are variable even within populations, including the bands curving or breaking into discontinuous lines or spots.
Hyperolius swynnertoni | Description
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
Random distribution, also known as unpredictable spacing, is the least common form of distribution in nature and occurs when the members of a given species are found in environments in which the position of each individual is independent of the other individuals: they neither attract nor repel one another. Random distribution is rare in nature as biotic factors, such as the interactions with neighboring individuals, and abiotic factors, such as climate or soil conditions, generally cause organisms to be either clustered or spread. Random distribution usually occurs in habitats where environmental conditions and resources are consistent. This pattern of dispersion is characterized by the lack of any strong social interactions between species.
Species distribution | Random
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
However, this behaviour is not expected to be the result of thermal pulses or evolutionary changes, and the cause is unknown.
S Orionis | Variability
Vegetation patterns such as tiger bush and fir waves form for different reasons. Tiger bush consists of stripes of bushes on arid slopes in countries such as Niger where plant growth is limited by rainfall. Each roughly horizontal stripe of vegetation absorbs rainwater from the bare zone immediately above it. In contrast, 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.
Pattern formation | Vegetation patterns
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
Anaximenes used his observations and reasoning to provide causes for other natural phenomena on the earth as well. Earthquakes, he asserted, were the result either of lack of moisture, which causes the earth to break apart because of how parched it is, or of superabundance of water, which also causes cracks in the earth. In either case the earth becomes weakened by its cracks, so that hills collapse and cause earthquakes. Lightning is similarly caused by the violent separation of clouds by the wind, creating a bright, fire-like flash. Rainbows, on the other hand, are formed when densely compressed air is touched by the rays of the sun.
Anaximenes of Miletus | Other phenomena
In nature, organisms are neither distributed uniformly nor at random, forming instead some sort of spatial pattern. This is due to various energy inputs, disturbances, and species interactions that result in spatially patchy structures or gradients. This spatial variance in the environment creates diversity in communities of organisms, as well as in the variety of the observed biological and ecological events. The type of spatial arrangement present may suggest certain interactions within and between species, such as competition, predation, and reproduction. On the other hand, certain spatial patterns may also rule out specific ecological theories previously thought to be true.
Spatial ecology | Overview
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
It might have formed either through erosion of surrounding sediments by ocean currents or through isostatic subsidence.
Anton Dohrn Seamount | Geography and geomorphology
Patterned ground is the distinct and often symmetrical natural pattern of geometric shapes formed by ground material in periglacial regions. It is typically found in remote regions of the Arctic, Antarctica, and the Outback in Australia, but is also found anywhere that freezing and thawing of soil alternate; patterned ground has also been observed on Mars. The geometric shapes and patterns associated with patterned ground are often mistaken as artistic human creations. The mechanism of the formation of patterned ground had long puzzled scientists but the introduction of computer-generated geological models in the past 20 years has allowed scientists to relate it to frost heaving, the expansion that occurs when wet, fine-grained, and porous soils freeze.
Patterned ground | Introduction
The deformations were likely caused by the force of the rising flood waters that filled the trunks with sand, as indicated by the tendency for the deformations to be in the same direction as the ripple marks, towards the south-west.
Fossil Grove | Description
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
From most random initial patterns of living cells on the grid, observers will find the population constantly changing as the generations tick by. The patterns that emerge from the simple rules may be considered a form of mathematical beauty. Small isolated subpatterns with no initial symmetry tend to become symmetrical. Once this happens, the symmetry may increase in richness, but it cannot be lost unless a nearby subpattern comes close enough to disturb it. In a very few cases, the society eventually dies out, with all living cells vanishing, though this may not happen for a great many generations. Most initial patterns eventually burn out, producing either stable figures or patterns that oscillate forever between two or more states; many also produce one or more gliders or spaceships that travel indefinitely away from the initial location.
Conway's Game of Life | Iteration
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
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
Bird's eye is a type of figure that occurs within several kinds of wood, most notably in hard maple. It has a distinctive pattern that resembles tiny, swirling eyes disrupting the smooth lines of grain. It is somewhat reminiscent of a burl, but it is quite different: the small knots that make the burl are missing. It is not known what causes the phenomenon. Research into the cultivation of bird's eye maple has so far discounted the theories that it is caused by pecking birds deforming the wood grain or that an infecting fungus makes it twist. However, no one has demonstrated a complete understanding of any combination of climate, soil, tree variety, insects, viruses or genetic mutation that may produce the effect.
Bird's eye figure | Introduction
In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a painting, drawing, tapestry, ceramic tiling or carpet, but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in the artwork. In mathematics, a tessellation is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps.
Pattern | Tilings
Deacon notes that the apparent patterns of causality exhibited by living systems seem to be in some ways the inverse of the causal patterns of non-living systems. In an attempt to find a solution to the philosophical problems associated with teleological explanations, Deacon returns to Aristotle's four causes and attempts to modernize them with thermodynamic concepts. Orthograde changes are caused internally. They are spontaneous changes. That is, orthograde changes are generated by the spontaneous elimination of asymmetries in a thermodynamic system in disequilibrium. Because orthograde changes are driven by the internal geometry of a changing system, orthograde causes can be seen as analogous to Aristotle's formal cause.
Incomplete Nature | Orthograde and contragrade
Fern leaves and Romanesco broccoli are two examples from nature." He points out an unexpected conclusion:
Benoit Mandelbrot | Developing "fractal geometry" and the Mandelbrot set
The fundamental macroecological question that the latitudinal diversity gradient depends on is "What causes patterns in species richness?". Species richness ultimately depends on whatever proximate factors are found to affect processes of speciation, extinction, immigration, and emigration. While some ecologists continue to search for the ultimate primary mechanism that causes the latitudinal richness gradient, many ecologists suggest instead this ecological pattern is likely to be generated by several contributory mechanisms (Gaston and Blackburn 2000, Willig et al. 2003, Rahbek et al. 2007). For now, the debate over the cause of the latitudinal diversity gradient will continue until a groundbreaking study provides conclusive evidence, or there is general consensus that multiple factors contribute to the pattern.
Latitudinal gradients in species diversity | Conclusion
Basaltic lava flows often display columnar jointing as a result of contraction forces causing cracks as the lava cools. The extensive crack networks that develop often produce hexagonal columns of lava. One example of such an array of columns is the Giant's Causeway in Northern Ireland. Tessellated pavement, a characteristic example of which is found at Eaglehawk Neck on the Tasman Peninsula of Tasmania, is a rare sedimentary rock formation where the rock has fractured into rectangular blocks. Other natural patterns occur in foams; these are packed according to Plateau's laws, which require minimal surfaces. Such foams present a problem in how to pack cells as tightly as possible: in 1887, Lord Kelvin proposed a packing using only one solid, the bitruncated cubic honeycomb with very slightly curved faces.
Tessellation | In nature
Complex hydrographical patterns with anticyclones and Taylor columns cause water flow around the summit. Water eddies tend to disrupt this flow. A bottom trawling experiment conducted during research brought up large orange roughy ("Hoplostethus atlanticus") aggregations, as well as bycatch of benthic fauna including sponges, gorgonians, and scleractinian corals.
Sedlo Seamount | Introduction
A speckle pattern is produced by the mutual interference of a set of coherent wavefronts. Although this phenomenon has been investigated by scientists since the time of Newton, speckles have come into prominence since the invention of the laser. They have been used in a variety of applications in microscopy, imaging, and optical manipulation. Speckle patterns typically occur in diffuse reflections of monochromatic light such as laser light. Such reflections may occur on materials such as paper, white paint, rough surfaces, or in media with a large number of scattering particles in space, such as airborne dust or in cloudy liquids.
Speckle pattern | Introduction
By dry season, large cushion of litter cover the floor because of increase in abscission rate of some plants such as "Musanga cecropioides", "Hallea ledermannii", "Calamus deeratus", "Gmelina arborea", "Raphia" spp. and "Elaeis guineensis".
Finima Nature Park | Flora
These minute fissures and larger gaps are primarily caused by jointing within the rocks. Joints are caused by tectonic, or mountain-building forces that move and stress rocks, causing them to fracture. The resulting cracks provide an inlet for water, which slowly dissolves the rocks and allows space for ice crystals to freeze and thaw during the seasonal cycles, further pushing the rocks apart. Eventually, plants and trees also grow up through crevasses in the rocks and can exert considerable pressure as they grow, forcing even larger gaps to form. Gravity and erosion work together to slowly level the landscape by breaking the rock into ever smaller pieces and transporting it away.
Bilger's Rocks | Formation
Rather, the translation of Aristotle's that is nearest to current ordinary language is "explanation." In "Physics" II.3 and "Metaphysics" V.2, Aristotle holds that there are four kinds of answers to "why" questions: The four "causes" are not mutually exclusive. For Aristotle, several, preferably four, answers to the question "why" have to be given to explain a phenomenon and especially the actual configuration of an object. For example, if asking why a table is such and such, a complete explanation, taking into account the four causes, would sound like this: This table is solid and brown because it is made of wood (matter), it does not collapse because it has four legs of equal length (form), it is as such because a carpenter made it starting from a tree (agent), it has these dimensions because it is to be used by men and women (end).
Four causes | Introduction
There is a well-documented global pattern that correlates decreasing plant and animal diversity with increasing latitude, that is to say, there are fewer species as one moves towards the poles. The cause of this pattern is one of the greatest puzzles for ecologists today. Theories for its explanation include energy availability, climatic variability, disturbance, competition, etc. Despite this global diversity gradient, this pattern can be weak for freshwater systems compared to global marine and terrestrial systems. This may be related to size, as Hillebrand and Azovsky found that smaller organisms (protozoa and plankton) did not follow the expected trend strongly, while larger species (vertebrates) did.
Lake ecosystem | Latitudinal patterns
This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.
Rainbow | Introduction
Overabundance may occur naturally, for example after weather events such as a period of high rainfall in which habitat conditions become optimal. However, other contributing factors include:
Overabundant species | Causes
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 coast is an example of a naturally occurring fractal, since it retains similar-appearing complexity at every level from the view of a satellite to a microscopic examination of how the water laps up against individual grains of sand. The branching of trees, which enables small twigs to stand in for full trees in dioramas, is another example. Because fractals can generate the appearance of patterns in nature, they have a beauty and familiarity not typically seen with mathematically generated functions. Fractals have also found a place in computer-generated movie effects, where their ability to create complex curves with fractal symmetries results in more realistic virtual worlds.
Symmetry (geometry) | Scale symmetry and fractals
Seiches are often imperceptible to the naked eye, and observers in boats on the surface may not notice that a seiche is occurring due to the extremely long wavelengths. The effect is caused by resonances in a body of water that has been disturbed by one or more factors, most often meteorological effects (wind and atmospheric pressure variations), seismic activity, or tsunamis. Gravity always seeks to restore the horizontal surface of a body of liquid water, as this represents the configuration in which the water is in hydrostatic equilibrium. Vertical harmonic motion results, producing an impulse that travels the length of the basin at a velocity that depends on the depth of the water.
Seiche | Causes and nature
The appearance of symmetry can be obliterated if the proliferation of the melanocytes (pigment cells) within the developing spots is so great that the sizes of the spots increase to the point that some of the spots merge, leaving only small areas of the white background among the spots and at the tips of the extremities. Animals with this pattern may include birds, cats, cattle, dogs, foxes, horses, cetaceans, deer, pigs, and snakes. Some animals also exhibit colouration of the irises of the eye that match the surrounding skin (blue eyes for pink skin, brown for dark). The underlying genetic cause is related to a condition known as leucism.
Piebald | Introduction
In applied mathematics, a Gilbert tessellation or random crack network is a mathematical model for the formation of mudcracks, needle-like crystals, and similar structures. It is named after Edgar Gilbert, who studied this model in 1967. In Gilbert's model, cracks begin to form at a set of points randomly spread throughout the plane according to a Poisson distribution. Then, each crack spreads in two opposite directions along a line through the initiation point, with the slope of the line chosen uniformly at random. The cracks continue spreading at uniform speed until they reach another crack, at which point they stop, forming a T-junction.
Gilbert tessellation | Introduction