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Fractal Canopy
In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely.Bello, Ignacio; Kaul, Anton; and Britton, Jack R. (2013). ''Topics in Contemporary Mathematics'', p.511. Cengage Learning. . Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments. A fractal canopy must have the following three properties: #The angle between any two neighboring line segments is the same throughout the fractal. #The ratio of lengths of any two consecutive line segments is constant. #Points all the way at the end of the smallest line segments are interconnected, which is to say the entire figure is a Graph (discrete mathematics)#Connected graph, connected graph. The pulmonary system used by humans to breat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal Canopy
In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely.Bello, Ignacio; Kaul, Anton; and Britton, Jack R. (2013). ''Topics in Contemporary Mathematics'', p.511. Cengage Learning. . Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments. A fractal canopy must have the following three properties: #The angle between any two neighboring line segments is the same throughout the fractal. #The ratio of lengths of any two consecutive line segments is constant. #Points all the way at the end of the smallest line segments are interconnected, which is to say the entire figure is a Graph (discrete mathematics)#Connected graph, connected graph. The pulmonary system used by humans to breat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscous Fingering
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oracle Thinkquest
ThinkQuest was an educational website, created 1996 and intended for primary and secondary schools. Beginning 2002 it was owned by the Oracle Education Foundation and was known as Oracle ThinkQuest. History ThinkQuest was created in 1996 by Allan H. Weis as part of his nonprofit Advanced Network and Services. The website and competition were acquired by the Oracle Education Foundation in 2002. Prior to being acquired by the Oracle Education Foundation, April Wennerstrom (née Buther) led the international training and evaluation program for the competition and worked with a cadre of international educators and judges to identify scholarship recipients. During its time under ANS' leadership, the organization gave over $1.5 million dollars annually for scholarships and support for the student-created sites and program participants spanned over 75 countries and six continents. As of July 1, 2013, the ThinkQuest initiative was discontinued.http://www.thinkquest.org/en/ -- or, the arc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lichtenberg Figure
A Lichtenberg figure (German ''Lichtenberg-Figuren''), or Lichtenberg dust figure, is a branching electric discharge that sometimes appears on the surface or in the interior of insulating materials. Lichtenberg figures are often associated with the progressive deterioration of high voltage components and equipment. The study of planar Lichtenberg figures along insulating surfaces and 3D electrical trees within insulating materials often provides engineers with valuable insights for improving the long-term reliability of high-voltage equipment. Lichtenberg figures are now known to occur on or within solids, liquids, and gases during electrical breakdown. Lichtenberg figures are natural phenomena which exhibit fractal properties. History Lichtenberg figures are named after the German physicist Georg Christoph Lichtenberg, who originally discovered and studied them. When they were first discovered, it was thought that their characteristic shapes might help to reveal the nature ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dendrite (crystal)
A crystal dendrite is a crystal that develops with a typical multi-branching form. The name comes from the Greek word dendron (δενδρον) which means "tree", since the crystal's structure resembles that of a tree. These crystals can be synthesised by using a supercooled pure liquid, however they are also quite common in nature. The most common crystals in nature exhibit dendritic growth are snowflakes and frost on windows, but many minerals and metals can also be found in dendritic structures. History Maximum velocity principle The first dendritic patterns were discovered in palaeontology and are often mistaken for fossils because of their appearance. The first theory for the creation of these patterns was published by Nash and Glicksman in 1974, they used a very mathematical method and derived a non-linear integro-differential equation for a classical needle growth. However they only found an inaccurate numerical solution close to the tip of the needle and they f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Tree
In probability theory, the Brownian tree, or Aldous tree, or Continuum Random Tree (CRT) is a special case from random real trees which may be defined from a Brownian excursion. The Brownian tree was defined and studied by David Aldous in three articles published in 1991 and 1993. This tree has since then been generalized. This random tree has several equivalent definitions and constructions: using sub-trees generated by finitely many leaves, using a Brownian excursion, Poisson separating a straight line or as a limit of Galton-Watson trees. Intuitively, the Brownian tree is a binary tree whose nodes (or branching points) are dense in the tree; which is to say that for any distinct two points of the tree, there will always exist a node between them. It is a fractal object which can be approximated with computers or by physical processes with dendritic structures. Definitions The following definitions are different characterisations of a Brownian tree, they are taken from Ald ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and "rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Breakdown
Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating materials undergo breakdown when the electric field caused by an applied voltage exceeds the material's dielectric strength. The voltage at which a given insulating object becomes conductive is called its breakdown voltage and in addition to its dielectric strength depends on its size and shape, and the location on the object at which the voltage is applied. Under sufficient electrical potential, electrical breakdown can occur within solids, liquids, or gases (and theoretically even in a vacuum). However, the specific breakdown mechanisms are different for each kind of dielectric medium. Electrical breakdown may be a momentary event (as in an electrostatic discharge), or may lead to a continuous electric arc if protective devices fail to int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blood Vessel
The blood vessels are the components of the circulatory system that transport blood throughout the human body. These vessels transport blood cells, nutrients, and oxygen to the tissues of the body. They also take waste and carbon dioxide away from the tissues. Blood vessels are needed to sustain life, because all of the body's tissues rely on their functionality. There are five types of blood vessels: the arteries, which carry the blood away from the heart; the arterioles; the capillaries, where the exchange of water and chemicals between the blood and the tissues occurs; the venules; and the veins, which carry blood from the capillaries back towards the heart. The word ''vascular'', meaning relating to the blood vessels, is derived from the Latin ''vas'', meaning vessel. Some structures – such as cartilage, the epithelium, and the lens and cornea of the eye – do not contain blood vessels and are labeled ''avascular''. Etymology * artery: late Middle English; from Latin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
H Tree
In fractal geometry, the H tree is a fractal tree structure constructed from perpendicular line segments, each smaller by a factor of the square root of 2 from the next larger adjacent segment. It is so called because its repeating pattern resembles the letter "H". It has Hausdorff dimension 2, and comes arbitrarily close to every point in a rectangle. Its applications include VLSI design and microwave engineering. Construction An H tree can be constructed by starting with a line segment of arbitrary length, drawing two shorter segments at right angles to the first through its endpoints, and continuing in the same vein, reducing (dividing) the length of the line segments drawn at each stage by \sqrt2. A variant of this construction could also be defined in which the length at each iteration is multiplied by a ratio less than 1/\sqrt2, but for this variant the resulting shape covers only part of its bounding rectangle, with a fractal boundary. An alternative process that gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. In wider definitions, the taller palms, tree ferns, bananas, and bamboos are also trees. Trees are not a taxonomic group but include a variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some reaching several thousand years old. Trees have been in existence for 370 million years. It is estimated that there are some three trillion mature trees in the world. A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulmonary System
The respiratory system (also respiratory apparatus, ventilatory system) is a biological system consisting of specific organs and structures used for gas exchange in animals and plants. The anatomy and physiology that make this happen varies greatly, depending on the size of the organism, the environment in which it lives and its evolutionary history. In land animals the respiratory surface is internalized as linings of the lungs. Gas exchange in the lungs occurs in millions of small air sacs; in mammals and reptiles these are called alveoli, and in birds they are known as atria. These microscopic air sacs have a very rich blood supply, thus bringing the air into close contact with the blood. These air sacs communicate with the external environment via a system of airways, or hollow tubes, of which the largest is the trachea, which branches in the middle of the chest into the two main bronchi. These enter the lungs where they branch into progressively narrower secondary and terti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
