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The science ofpattern formation deals with the visible, (statistically) orderly outcomes ofself-organization and the common principles behind similarpatterns in nature.
Indevelopmental biology, pattern formation refers to the generation of complex organizations ofcell fates in space and time. The role of genes in pattern formation is an aspect ofmorphogenesis, the creation of diverseanatomies from similar genes, now being explored in the science ofevolutionary developmental biology or evo-devo. The mechanisms involved are well seen in the anterior-posterior patterning ofembryos from themodel organismDrosophila melanogaster (a fruit fly), one of the first organisms to have its morphogenesis studied, and in theeyespots of butterflies, whose development is a variant of the standard (fruit fly) mechanism.
Examples of pattern formation can be found in biology, physics, and other scientific fields,[1] and can readily be simulated with computer graphics, as described in turn below.
Biological patterns such asanimal markings, the segmentation of animals, andphyllotaxis are formed in different ways.[2]
Indevelopmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in anembryo assume complex forms and functions.[3]Embryogenesis, such asof the fruit flyDrosophila, involves coordinatedcontrol of cell fates.[4][5][6] Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along amorphogen gradient, followed by short-distance cell-to-cell communication throughcell-signaling pathways to refine the initial pattern. In this context, a field of cells is the group of cells whose fates are affected by responding to the same set of positional information cues. This conceptual model was first described as theFrench flag model in the 1960s.[7][8] More generally, the morphology of organisms is patterned by the mechanisms ofevolutionary developmental biology, such aschanging the timing and positioning of specific developmental events in the embryo.[9]
Possible mechanisms of pattern formation in biological systems include the classicalreaction–diffusion model proposed byAlan Turing[10] and the more-recently-foundelastic instability mechanism which is thought to be responsible for the fold patterns on thecerebral cortex of higher animals, among other things.[11][12]Cellular automata andneural network models have both been proposed to explain the patterns on some marine mollusc shells such as those of the genusConus.[13][14][15][16]
Bacterial colonies show alarge variety of patterns formed during colony growth. The resulting shapes depend on the growth conditions. In particular, stresses (hardness of the culture medium, lack of nutrients, etc.) enhance the complexity of the resulting patterns.[17] Other organisms such asslime moulds display remarkable patterns caused by the dynamics of chemical signaling.[18] Cellular embodiment (elongation and adhesion) can also have an impact on the developing patterns.[19]
Vegetation patterns such astiger bush[20] andfir waves[21] form for different reasons. Tiger bush consists of stripes of bushes on arid slopes in countries such asNiger where plant growth is limited by rainfall. Each roughly horizontal stripe of vegetation absorbs rainwater from the bare zone immediately above it.[20] 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.[21] 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.[22][23]
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Pattern formation has been well-studied in chemistry and chemical engineering, including both temperature and concentration patterns.[24] TheBrusselator model developed byIlya Prigogine and collaborators is one such example that exhibitsTuring instability.[25] Pattern formation in chemical systems often involvesoscillatory chemical kinetics orautocatalytic reactions[26] such as theBelousov–Zhabotinsky orBriggs–Rauscher reactions. In industrial applications such as chemical reactors, pattern formation can lead to temperature hot spots, which can reduce the yield or create hazardous safety problems such as athermal runaway.[27][24] The emergence of pattern formation can be studied by mathematical modeling and simulation of the underlyingreaction-diffusion system.[24][26]
Similarly as in chemical systems, patterns can develop in a weakly ionized plasma of a positive column of a glow discharge. In such cases, creation and annihilation of charged particles due to collisions of atoms corresponds to reactions in chemical systems. Corresponding processes are essentially non-linear and lead in a discharge tube to formation of striations with regular or random character.[28][29]
Other chemical patterns includeLiesegang rings.
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When a planar body of fluid under the influence of gravity is heated from below,Rayleigh-Bénard convection can form organized cells in hexagons or other shapes. These patterns form on thesurface of the Sun and in themantle of the Earth as well as during more pedestrian processes. The interaction between rotation, gravity, and convection can cause planetary atmospheres to form patterns, as is seen inSaturn's hexagon and theGreat Red Spot and stripes ofJupiter. The same processes cause orderedcloud formations on Earth, such asstripes androlls.
In the 1980s,Lugiato and Lefever developed a model of light propagation in an optical cavity that results in pattern formation by the exploitation of nonlinear effects.
Precipitating andsolidifying materials can crystallize into intricate patterns, such as those seen insnowflakes anddendritic crystals.
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Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed.
Some types ofautomata have been used to generate organic-lookingtextures for more realisticshading of3D objects.[30][31]
A popular Photoshop plugin,KPT 6, included a filter called "KPT reaction". Reaction producedreaction–diffusion style patterns based on the supplied seed image.
A similar effect to the KPT reaction can be achieved withconvolution functions indigital image processing, with a little patience, by repeatedlysharpening andblurring an image in a graphics editor. If other filters are used, such asemboss oredge detection, different types of effects can be achieved.
Computers are often used tosimulate the biological, physical, or chemical processes that lead to pattern formation, and they can display the results in a realistic way. Calculations using models likereaction–diffusion orMClone are based on the actual mathematical equations designed by the scientists to model the studied phenomena.
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