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Natural Patterns
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. 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 whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Desert Ultra - Sand Dunes
''The'' () is a grammatical article in English, denoting persons or things already mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the most frequently used word in the English language; studies and analyses of texts have found it to account for seven percent of all printed English-language words. It is derived from gendered articles in Old English which combined in Middle English and now has a single form used with pronouns of any gender. The word can be used with both singular and plural nouns, and with a noun that starts with any letter. This is different from many other languages, which have different forms of the definite article for different genders or numbers. Pronunciation In most dialects, "the" is pronounced as (with the voiced dental fricative followed by a schwa) when followed by a consonant sound, and as (homophone of pronoun '' thee'') when followed by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Plateau
Joseph Antoine Ferdinand Plateau (14 October 1801 – 15 September 1883) was a Belgian physicist and mathematician. He was one of the first people to demonstrate the illusion of a moving image. To do this, he used counterrotating disks with repeating drawn images in small increments of motion on one and regularly spaced slits in the other. He called this device of 1832 the phenakistiscope. Biography Plateau was born in Brussels. His father, Antoine Plateau ( fr) born in Tournai, was a talented flower painter. At the age of six, the younger Plateau already could read, making him a child prodigy in those times. While attending primary school, he was particularly impressed by a lesson of physics; enchanted by the experiments he observed, he vowed to discover their secrets someday. Plateau spent his school holidays in Marche-les-Dames, with his uncle and his family; his cousin and playfellow was Auguste Payen, who later became an architect and the principal designer of the Belgia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractals
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called Affine geometry, affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they Scaling (geometry), scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benoît Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristid Lindenmayer
Aristid Lindenmayer (17 November 1925 – 30 October 1989) was a Hungarian biologist. In 1968 he developed a type of formal languages that is today called L-systems or Lindenmayer Systems. Using those systems Lindenmayer modelled the behaviour of cells of plants. L-systems nowadays are also used to model whole plants. Lindenmayer worked with yeast and filamentous fungi and studied the growth patterns of various types of algae, such as the blue/green bacteria ''Anabaena catenula''. Originally the L-systems were devised to provide a formal description of the development of such simple multicellular organisms, and to illustrate the neighbourhood relationships between plant cells. Later on, this system was extended to describe higher plants and complex branching structures. Career Lindenmayer studied chemistry and biology at the Eötvös Loránd University of Budapest from 1943 to 1948. He received his Ph.D. in plant physiology in 1956 at the University of Michigan. In 1968 he b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Patterns
The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. Overview In his classic paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Prior to the discovery of this instability mechanism arising due to unequal diffusion coefficients of the two substances, diffusional effects are always presumed to have stabilizing influences on the system. Turing hypothesized that the resulting wavelike patterns are the chemical basis of morphogenesis. Turing patterning is often found in combination with other patterns: vertebrate limb development is one of the many phenotypes exhibiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morphogenesis
Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of developmental biology along with the control of tissue growth and patterning of cellular differentiation. The process controls the organized spatial distribution of cells during the embryonic development of an organism. Morphogenesis can take place also in a mature organism, such as in the normal maintenance of tissue by stem cells or in regeneration of tissues after damage. Cancer is an example of highly abnormal and pathological tissue morphogenesis. Morphogenesis also describes the development of unicellular life forms that do not have an embryonic stage in their life cycle. Morphogenesis is essential for the evolution of new forms. Morphogenesis is a mechanical process involving forces that generate mechanical stress, strain, and mov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence. Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Arcy Thompson
Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948) was a Scottish biologist, mathematician and classics scholar. He was a pioneer of mathematical and theoretical biology, travelled on expeditions to the Bering Strait and held the position of Professor of Natural History at University College, Dundee for 32 years, then at St Andrews for 31 years. He was elected a Fellow of the Royal Society, was knighted, and received the Darwin Medal and the Daniel Giraud Elliot Medal. Thompson is remembered as the author of the 1917 book '' On Growth and Form'', which led the way for the scientific explanation of morphogenesis, the process by which patterns and body structures are formed in plants and animals. Thompson's description of the mathematical beauty of nature, and the mathematical basis of the forms of animals and plants, stimulated thinkers as diverse as Julian Huxley, C. H. Waddington, Alan Turing, René Thom, Claude Lévi-Strauss, Eduardo Paolozzi, Le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marine Biology
Marine biology is the scientific study of the biology of marine life, organisms in the sea. Given that in biology many phyla, families and genera have some species that live in the sea and others that live on land, marine biology classifies species based on the environment rather than on taxonomy. A large proportion of all life on Earth lives in the ocean. The exact size of this ''large proportion'' is unknown, since many ocean species are still to be discovered. The ocean is a complex three-dimensional world covering approximately 71% of the Earth's surface. The habitats studied in marine biology include everything from the tiny layers of surface water in which organisms and abiotic items may be trapped in surface tension between the ocean and atmosphere, to the depths of the oceanic trenches, sometimes 10,000 meters or more beneath the surface of the ocean. Specific habitats include estuaries, coral reefs, kelp forests, seagrass meadows, the surrounds of seamounts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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