The science of pattern formation deals with the visible, (

statistically Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...

) orderly outcomes of self-organization and the common principles behind similar

patterns in nature 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, wave ...

. In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. 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

embryo An embryo is an initial stage of development of a multicellular organism. In organisms that reproduce sexually, embryonic development is the part of the life cycle that begins just after fertilization of the female egg cell by the male sperm ...

s from the model organism ''

Drosophila melanogaster ''Drosophila melanogaster'' is a species of fly (the taxonomic order Diptera) in the family Drosophilidae. The species is often referred to as the fruit fly or lesser fruit fly, or less commonly the " vinegar fly" or " pomace fly". Starting with ...

'' (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.

Patterns in nature

Examples of pattern formation can be found in biology, physics, and science, and can readily be simulated with computer graphics, as described in turn below.

Biology

Biological patterns such as

animal markings Animal coloration is the general appearance of an animal resulting from the reflection or emission of light from its surfaces. Some animals are brightly coloured, while others are hard to see. In some species, such as the peafowl, the male h ...

, the segmentation of animals, and phyllotaxis are formed in different ways. In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an

assume complex forms and functions. Embryogenesis, such as of the fruit fly ''Drosophila'', involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell 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 positional information cues. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo. Possible mechanisms of pattern formation in biological systems include the classical reaction–diffusion model proposed by

Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical c ...

and the more recently found elastic instability mechanism which is thought to be responsible for the fold patterns on the

cerebral cortex The cerebral cortex, also known as the cerebral mantle, is the outer layer of neural tissue of the cerebrum of the brain in humans and other mammals. The cerebral cortex mostly consists of the six-layered neocortex, with just 10% consisting o ...

of higher animals, among other things.

Growth of colonies

Bacterial colonies show a large 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. Other organisms such as slime moulds display remarkable patterns caused by the dynamics of chemical signaling. Cellular embodiment (elongation and adhesion) can also have an impact on the developing patterns.

Vegetation patterns

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 ) , official_languages = , languages_type = National languages The Brusselator model developed by Ilya Prigogine and collaborators is one such example that exhibits Turing instability. Pattern formation in chemical systems often involve oscillatory chemical kinetics or autocatalytic reactions such as

Belousov–Zhabotinsky reaction A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. The only common element i ...

or Briggs–Rauscher reaction. 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 a thermal runaway. The emergence of pattern formation can be studied by mathematical modeling and simulation of the underlying reaction-diffusion system. 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. *

* Liesegang rings *

Ionization waves Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule i ...

Physics

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 the surface of the sun and in the

mantle of the Earth Earth's mantle is a layer of silicate rock between the crust and the outer core. It has a mass of 4.01 × 1024 kg and thus makes up 67% of the mass of Earth. It has a thickness of making up about 84% of Earth's volume. It is predominantly so ...

as well as during more pedestrian processes. The interaction between rotation, gravity, and convection can cause planetary atmospheres to form patterns, as is seen in

Saturn's hexagon Saturn's hexagon is a persistent approximately hexagonal cloud pattern around the north pole of the planet Saturn, located at about 78°N. The sides of the hexagon are about long, which is about longer than the diameter of Earth. The hexagon ...

and the Great Red Spot and stripes of

Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandt ...

. The same processes cause ordered

cloud formations The list of cloud types groups all genera as ''high'' (cirro-, cirrus), ''middle'' (alto-), ''multi-level'' (nimbo-, cumulo-, cumulus), and ''low'' (strato-, stratus). These groupings are determined by the altitude level or levels in the troposphe ...

on Earth, such as stripes and rolls. 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 and solidifying materials can crystallize into intricate patterns, such as those seen in snowflakes and dendritic crystals.

Mathematics

Sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere pack ...

s and coverings. Mathematics underlies the other pattern formation mechanisms listed.

Computer graphics

Some types of automata have been used to generate organic-looking textures for more realistic shading of 3d objects. 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 the 'KPT reaction' can be achieved with convolution functions in digital image processing, with a little patience, by repeatedly sharpening and blurring an image in a graphics editor. If other filters are used, such as emboss or edge detection, different types of effects can be achieved. Computers are often used to simulate the biological, physical or chemical processes that lead to pattern formation, and they can display the results in a realistic way. Calculations using models like reaction–diffusion or

MClone MClone, or Clonal Mosaic, is a pattern formation algorithm proposed in 1998 used specially for simulating the visible patches of color in the fur of giraffes and members of the ''Felidae'' of the mammalians. It was primarily proposed as a 2D mode ...

are based on the actual mathematical equations designed by the scientists to model the studied phenomena.

References

Bibliography

External links

''SpiralZoom.com''
an educational website about the science of pattern formation, spirals in nature, and spirals in the mythic imagination.
'15-line Matlab code'
A simple 15-line Matlab program to simulate 2D pattern formation for reaction-diffusion model. {{DEFAULTSORT:Pattern Formation Developmental biology Articles containing video clips