Fractal analysis
Encyclopedia
Fractal analysis is the modelling of data by fractals.
It consists of methods to assign a fractal dimension
and other fractal characteristics to a signal, dataset or object which may be sound, images, molecules, networks or other data.
Fractal analysis is now widely used in all areas of science
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It consists of methods to assign a fractal dimension
Fractal dimension
In fractal geometry, the fractal dimension, D, is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. There are many specific definitions of fractal dimension. The most important theoretical fractal...
and other fractal characteristics to a signal, dataset or object which may be sound, images, molecules, networks or other data.
Fractal analysis is now widely used in all areas of science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
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Applications
Applications of fractal analysis include:- Classification of histopathologyHistopathologyHistopathology refers to the microscopic examination of tissue in order to study the manifestations of disease...
slides in medicineMedicineMedicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness.... - Fractal landscapeFractal landscapeA fractal landscape is a surface generated using a stochastic algorithm designed to produce fractal behaviour that mimics the appearance of natural terrain...
or CoastCoastA coastline or seashore is the area where land meets the sea or ocean. A precise line that can be called a coastline cannot be determined due to the dynamic nature of tides. The term "coastal zone" can be used instead, which is a spatial zone where interaction of the sea and land processes occurs...
line complexity - Enzyme/enzymology (Michaelis-Menten kineticsMichaelis-Menten kineticsIn biochemistry, Michaelis–Menten kinetics is one of the simplest and best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating...
) - An Equation of State for the Coexistence of Stability and Flexibility in Proteins
- Generation of new musicAlgorithmic compositionAlgorithmic composition is the technique of using algorithms to create music.Algorithms have been used to compose music for centuries; the procedures used to plot voice-leading in Western counterpoint, for example, can often be reduced to algorithmic determinacy...
- Generation of various art formsFractal artFractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media. Fractal art developed from the mid 1980s onwards. It is a genre of computer art and digital art which are part of new media art...
- Signal and image compressionFractal compressionFractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image...
- SeismologySeismologySeismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake effects, such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic,...
- Wave propagation in self-similar (fractal) media
- Fractal in soil mechanicsFractal in soil mechanicsThe fractal approach to soil mechanics is a new line of thought. There are several problems in soil mechanics which can be dealt with by applying a fractal approach. One of these problems is the determination of soil-water-characteristic curve...
- Computer and video game designGame designGame design, a subset of game development, is the process of designing the content and rules of a game in the pre-production stage and design of gameplay, environment, storyline, and characters during production stage. The term is also used to describe both the game design embodied in a game as...
, especially computer graphicsComputer graphicsComputer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
for organicLifeLife is a characteristic that distinguishes objects that have signaling and self-sustaining processes from those that do not, either because such functions have ceased , or else because they lack such functions and are classified as inanimate...
environments and as part of procedural generationProcedural generationProcedural generation is a widely used term in the production of media; it refers to content generated algorithmically rather than manually. Often, this means creating content on the fly rather than prior to distribution... - Fractography and fracture mechanicsFracture mechanicsFracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.In...
- Fractal antennaFractal antennaA fractal antenna is an antenna that uses a fractal, self-similar design to maximize the length, or increase the perimeter , of material that can receive or transmit electromagnetic radiation within a given total surface area or volume.Such fractal antennas are also referred to as multilevel and...
s — Small size antennas using fractal shapes - Small angle scattering theory of fractally rough systemsSAXSSmall-angle scattering is a fundamental method for structure analysis of materials, including biological materials. Small-angle scattering allows one to study the structure of a variety of objects such as solutions of biological macromolecules, nanocomposites, alloys, synthetic polymers, etc...
- T-shirtT-shirtA T-shirt is a style of shirt. A T-shirt is buttonless and collarless, with short sleeves and frequently a round neck line....
s and other fashionFashionFashion, a general term for a currently popular style or practice, especially in clothing, foot wear, or accessories. Fashion references to anything that is the current trend in look and dress up of a person... - Generation of patterns for camouflage, such as MARPATMARPATMARPAT is a digital camouflage pattern in use with the United States Marine Corps, introduced with the Marine Corps Combat Utility Uniform , which replaced the Camouflage Utility Uniform. The pattern is formed by a number of small rectangular pixels of color...
- Digital sundialDigital sundialA digital sundial is a clock that indicates the current time with numerals formed by the sunlight striking it. Like a classical sundial, the device is purely passive and contains no moving parts. It uses no electricity nor other artificial sources of energy....
- Technical analysisTechnical analysisIn finance, technical analysis is security analysis discipline for forecasting the direction of prices through the study of past market data, primarily price and volume. Behavioral economics and quantitative analysis incorporate technical analysis, which being an aspect of active management stands...
of price series (see Elliott wave principleElliott wave principleThe Elliott Wave Principle is a form of technical analysis that some traders use to analyze financial market cycles and forecast market trends by identifying extremes in investor psychology, highs and lows in prices, and other collective factors...
) - Fractal analysis in music