The science of pattern formation deals with the visible, (statistically) orderly outcomes of
self-organisationand the common principles behind similar patterns.
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 best understood in the anterior-posterior patterning of embryos from the model organism "Drosophila melanogaster" (fruit fly).
Animal markings, segmentation of animals, phyllotaxis, neuronal activation patterns like tonotopy, predator-prey equations' trajectories.
In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue assume complex forms and functions by coordinated cell fate control [http://cistron.ca/1_pattern_formation.shtml Essay: Pattern formation in fruit fly wings] [http://www.biologie.uni-hamburg.de/b-online/e28_1/pattern.htm Essay: Biological pattern formation] . Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a
morphogengradient, followed by short distance cell-to-cell communication through cell signalingpathways 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 positional information cues. This conceptual model was first described as French flag modelin the 1960s.
Anterior-posterior axis patterning in "Drosophila"
One of the best understood examples of pattern formation is the patterning along the future head to tail (antero-posterior) axis of the fruit fly "
Drosophila melanogaster". The development of "Drosophila" is particularly well studied, and it is representative of a major class of animals, the insects or insecta. Other multicellular organisms sometimes use similar mechanisms for axis formation, although the relative importance of signal transfer between the earliest cells of many developing organisms is greater than in the example described here.
Growth of Bacterial Colonies
Bacterial colonies show a large variety of beautiful patterns formed during colony growth. Experiments show that the resulting shapes depend on the growth conditions. In particular stresses (hardness of the culture medium, lack of nutrients, etc) seem to enhance the complexity of the resulting patterns.
reaction-diffusionsystems and Turing Patterns
Bénard cells, Laser, cloud formations in stripes or rolls. Ripples in icicles. Washboard patterns on dirtroads. Dendrites in solidification, liquid crystals.
[ [http://www.cc.gatech.edu/~turk/reaction_diffusion/reaction_diffusion.html Reaction-Diffusion ] ] [http://www.cs.cmu.edu/~aw/pdf/texture.pdf] .
A popular photoshop plugin, KPT 6, included a filter called 'KPT reaction'. Reaction produced reaction-diffusion style patterns based on the supplied seed image.
A similar effect to 'kpt reaction' can be achieved, with a little patience, by repeatedly sharpening and then blurring an image in many graphics applications. If other filters are used, such as emboss or
edge detection, different types of effects can be achieved.
The analysis of pattern-forming systems often consists of finding a
PDEmodel of the system (the Swift-Hohenberg equationis one such model) of the form
where "F" is generically a
nonlinear differential operator, and postulating solutions of the form
where the are complex amplitudes associated to different modes in the solution and the are the wave-vectors associated to a
lattice, e.g. a square or hexagonal lattice in two dimensions. There is in general no rigorous justification for this restriction to a lattice.
Symmetry considerations can now be taken into account, and evolution equations obtained for the complex amplitudes governing the solution. This reduction puts the problem into the form of a system of first-order
ODEs, which can be analysed using standard methods (see dynamical systems). The same formalism can also be used to analyse bifurcationsin pattern-forming systems, for example to analyse the formation of convectionrolls in a Rayleigh-Bénardexperiment as the temperature is increased.
Such analysis predicts many of the quantitative features of such experiments - for example, the ODE reduction predicts
hysteresisin convection experiments as patterns of rolls and hexagons compete for stability. The same hysteresis has been observed experimentally.
* [http://spiralzoom.com/Science/patternformation/patternformation.html "SpiralZoom.com"] , an educational website about the science of pattern formation, spirals in nature, and spirals in the mythic imagination.
* [http://www.texrd.com 'TexRD'] , a free software to experiment pattern formation with different kinds of reaction-diffusion models (simulations in 2 dimensions; basic interface with text parameters)
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pattern formation — paveikslo sukūrimas statusas T sritis radioelektronika atitikmenys: angl. pattern formation; pattern generation; patterning vok. Mustererzeugung, f; Strukturabbildung, f rus. образование рисунка, n; формирование рисунка, n pranc. définition du… … Radioelektronikos terminų žodynas
pattern formation — One of the classic problems in developmental biology is the way in which complex patterns are formed from an apparently uniform field of cells. Various hypotheses have been put forward, and there is now evidence for the existence of gradients of… … Dictionary of molecular biology
pattern formation mask — paveikslo sukūrimo kaukė statusas T sritis radioelektronika atitikmenys: angl. pattern formation mask vok. Strukturerzeugungsmaske, f rus. маска для формирования рисунка, f pranc. masque pour définition de dessin, m; masque pour définition de… … Radioelektronikos terminų žodynas
fine-pattern formation — mikroskopinio paveikslo sudarymas statusas T sritis radioelektronika atitikmenys: angl. fine pattern formation vok. Mikrostrukturerzeugung, f rus. образование микрорисунка, n; образование рисунка с элементами уменьшенных размеров, n pranc.… … Radioelektronikos terminų žodynas
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pattern generation — paveikslo sukūrimas statusas T sritis radioelektronika atitikmenys: angl. pattern formation; pattern generation; patterning vok. Mustererzeugung, f; Strukturabbildung, f rus. образование рисунка, n; формирование рисунка, n pranc. définition du… … Radioelektronikos terminų žodynas
formation du dessin — paveikslo sukūrimas statusas T sritis radioelektronika atitikmenys: angl. pattern formation; pattern generation; patterning vok. Mustererzeugung, f; Strukturabbildung, f rus. образование рисунка, n; формирование рисунка, n pranc. définition du… … Radioelektronikos terminų žodynas
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