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
Developmental biology is the study of the process by which animals and plants grow and develop. Developmental biology also encompasses the biology of Regeneration (biology), regeneration, asexual reproduction, metamorphosis, and the growth and di ...
, 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
Evolutionary developmental biology, informally known as evo-devo, is a field of biological research that compares the developmental biology, developmental processes of different organisms to infer how developmental processes evolution, evolved. ...
or evo-devo. The mechanisms involved are well seen in the anterior-posterior patterning of
embryos from the
model organism
A model organism is a non-human species that is extensively studied to understand particular biological phenomena, with the expectation that discoveries made in the model organism will provide insight into the workings of other organisms. Mo ...
''
Drosophila melanogaster
''Drosophila melanogaster'' is a species of fly (an insect of the Order (biology), 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", "pomace fly" ...
'' (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, the segmentation of animals, and
phyllotaxis
In botany, phyllotaxis () or phyllotaxy is the arrangement of leaf, leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature.
Leaf arrangement
The basic leaf#Arrangement on the stem, arrangements of leaves ...
are formed in different ways.
In
developmental biology
Developmental biology is the study of the process by which animals and plants grow and develop. Developmental biology also encompasses the biology of Regeneration (biology), regeneration, asexual reproduction, metamorphosis, and the growth and di ...
, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an
embryo assume complex forms and functions.
Embryogenesis
An embryo ( ) is the initial stage of development for 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 ...
, 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
In biology, cell signaling (cell signalling in British English) is the Biological process, process by which a Cell (biology), cell interacts with itself, other cells, and the environment. Cell signaling is a fundamental property of all Cell (biol ...
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
The French flag model is a conceptual definition of a morphogen, described by Lewis Wolpert in the 1960s. A morphogen is defined as a signaling molecule that acts directly on cells (not through serial induction) to produce specific cellular resp ...
in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of
evolutionary developmental biology
Evolutionary developmental biology, informally known as evo-devo, is a field of biological research that compares the developmental biology, developmental processes of different organisms to infer how developmental processes evolution, evolved. ...
, 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. He was highly influential in the development of theoretical computer ...
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. It is the largest site of Neuron, neural integration in the central nervous system, and plays ...
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
Niger, officially the Republic of the Niger, is a landlocked country in West Africa. It is a unitary state Geography of Niger#Political geography, bordered by Libya to the Libya–Niger border, north-east, Chad to the Chad–Niger border, east ...
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.][ 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.
]
Chemistry
Pattern formation has been well studied in chemistry and chemical engineering, including both temperature and concentration patterns. 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 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.
* Belousov–Zhabotinsky reaction
* Liesegang rings
* Ionization waves
]
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 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 and the Great Red Spot and stripes of Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined a ...
. The same processes cause ordered cloud formations 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
A snowflake is a single ice crystal that is large enough to fall through the Earth's atmosphere as snow.Knight, C.; Knight, N. (1973). Snow crystals. Scientific American, vol. 228, no. 1, pp. 100–107.Hobbs, P.V. 1974. Ice Physics. Oxford: C ...
and dendritic crystals.
Mathematics
Sphere packings 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
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two ...
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 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 (archived 14 May 2019)
'15-line Matlab code'
A simple 15-line Matlab program to simulate 2D pattern formation for reaction-diffusion model.
{{DEFAULTSORT:Pattern Formation
Developmental biology
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