Image Mandel zoom 00 mandelbrot set.jpg thumb The Mandelbrot set is a famous example of a fractal A fractal ... The Fractal Geometry of Nature publisher W.H. Freeman and Company. year 1982 isbn 0 7167 1186 9 ... function continuous but not differentiable however, the term wikt fractalfractal was coined by Beno t .... A mathematical fractal is based on an equation that undergoes iteration , a form of feedback ... glass illustrate fractal process development in a purely physical system A fractal often has the following features ref Cite book last Falconer first Kenneth title Fractal Geometry Mathematical Foundations ... fractal characteristics for instance, it is regular enough to be described in Euclidean terms. Images of fractals can be created using fractal generating software . Images produced by such software ... it is possible to zoom into a region of the fractal that does not exhibit any fractal properties ... today be considered fractal, when Karl Weierstrass gave an Weierstrass function example of a function ... fractal koch curve book&hl en&ei NGFNTfCeHofAgQeV3NDuDw&sa X&oi book result&ct result&resnum 1&ved 0CDYQ6AEwAA v onepage&q fractal 20koch 20curve 20book&f false author Clifford A. Pickover title The Math ... fractal curve, the L vy C curve . Georg Cantor also gave examples of subset s of the real line with unusual ... . Finally, in 1975 Mandelbrot coined the word fractal to denote an object whose Hausdorff ... many of them were based on recursion, leading to the popular meaning of the term fractal . ref cite book url http books.google.com books?id qDQjyuuDRxUC&pg PA1&lpg PA1&dq fractal history book&source ... result&resnum 9&ved 0CEwQ6AEwCA v onepage&q fractal 20history 20book&f false page 1 title Fractal ... A Julia set , a fractal related to the Mandelbrot set A class of examples is given by the Cantor set ... curve , and Koch snowflake Koch curve . Additional examples of fractals include the Lyapunov fractal ... space for a family of systems may be fractal as well. An interesting example is the Mandelbrot ... more details
notability date October 2010 Fractal Records is an independent French label created in September 1994 ... of Fractal Records. Catalogue Fractal Records Mainliner Psychedelic Polyhedron LP Fractal 001 1997 Igor Wakh vitch Donc... Coffret 6 CDs Fractal 002 1998 Seikazoku Outtakes 66 78 CD Fractal 003 1998 High Rise Durophet LP Fractal 004 1999 High Rise Durophet CD Fractal 005 1999 Frank Wright Quartet Center Of The World CD Bonus Tracks Fractal 006 1999 Frank Wright Quartet Last Polka In Nancy ? CD Bonus Tracks Fractal 007 1999 Michel Bulteau Rin ures CD Fractal 008 1999 Arthur Doyle & Sunny Murray Dawn Of A New Vibration CD Fractal 009 2000 Iannis Xenakis Persepolis CD Fractal 0X 2000 Kawabata & Pauvros Extr me Onction CD Fractal 011 2001 Ilitch Periodikmindtrouble 2 CDs Bonus Tracks Fractal 012 2001 Ilitch 10 Suicides 2 CDs Bonus Tracks Fractal 013 2001 Ruth Polaroid Roman Photo CD Bonus Tracks Fractal 014 2001 Iannis Xenakis Musique Electro Acoustique CD Fractal 015 2001 Fille Qui Mousse Se Taire Pour Une Femme Trop Belle CD Fractal 016 2001 Jacques Berrocal Musiq Musik CD Fractal 017 2002 Ohkami No Jikan Mort Nuit CD Fractal 018 2002 Musica Transonic Hard Rock Transonic CD Fractal 019 2002 Acid Mothers Temple & The Melting Paraiso UFO Univers Zen Ou De Z ro A Z ro CD Fractal 020 2002 Acid Mothers Temple & The Melting Paraiso UFO Electric Love Machine EP Single Fractal 0207 ... Fractal 020412 2003 Various Artists Amaterasu 2 CDs Fractal 021 2003 Knead This Melting Happiness I Want You To Realize That It Is Another Trap LP Fractal 023 2003 Ilitch Hors Temps Out Of Time CD Fractal 024 2004 Toho Sara Hourouurin CD Fractal 025 2004 Musique Concret Bringing Up Baby CD Fractal 026 2004 Asahito Nanjo Group Musica Contemporary Kagura Metaphysics CD Fractal 027 2004 Bernard Parmegiani JazzEx CD Unreleased Live Track Fractal 028 2004 Keiko Kojima Taikoku No Kage EP Single Fractal 029 2004 Mainliner Psychedelic Polyhedron CD Bonus Track Fractal 030 2004 Mahogany Brain Some Cocktail ... more details
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 . Applications Applications of fractal analysis include ref cite web url http library.thinkquest.org 26242 full ap ap.html title Applications accessdate 2007 10 21 ref Categorisation Classification of histopathology slides in medicine Fractal landscape or Coast line complexity Enzyme enzymology Michaelis Menten kinetics http prl.aps.org abstract PRL v100 i20 e208101 An Equation of State for the Coexistence of Stability and Flexibility in Proteins Algorithmic composition Generation of new music Fractal art Generation of various art forms Signal information theory Signal and Fractal compression image compression Seismology http fr.arxiv.org abs 0904.0780 Wave propagation in self similar fractal media Fractal in soil mechanics game design Computer and video game design , especially computer graphics for life organic environments and as part of procedural generation Fractography and fracture mechanics Fractal antenna s &mdash Small size antennas using fractal shapes SAXS Small angle scattering theory of fractally rough systems T shirt s and other fashion Generation of patterns for camouflage, such as MARPAT Digital sundial Technical analysis of price series see Elliott wave principle http www.brotherstechnology.com math fractal music.html Fractal analysis in music See also Multifractal Further reading http rsb.info.nih.gov ij plugins fraclac FLHelp Fractals.htm Fractals and Fractal Analysis http www.fch.vutbr.cz lectures imagesci download ejournal 01 O.Zmeskal.pdf Fractal analysis http www.trusoft.netmegs.com Benoit Fractal Analysis Software http www.physionet.org tutorials fmnc index.shtml Fractal Analysis Methods for Human Heartbeat and Gait Dynamics References Reflist added above ... more details
Image Box fractal.png thumb right 200px Vicsek fractal rotated In mathematics the Vicsek fractal , also known as Vicsek snowflake or box fractal ref MathWorld urlname BoxFractal title Box Fractal ref , arises from a construction similar to that of the Sierpinski carpet . The basic square is decomposed into nine smaller squares in the 3 by 3 grid. The four squares at the corners and the middle square are left, the other squares being removed. The process is repeated recursively for each of the five remaining subsquares. The Vicsek fractal is the set obtained at the limit of this procedure. The Hausdorff dimension of this fractal is log 5 log 3 1.46497. An alternative construction shown below in the left image is to remove the four corner squares and leave the middle square and the squares above, below, left and right of it. The two constructions produce identical limiting curves, but one is rotated by 45 degrees with respect to the other. gallery Image Box fractal2.PNG Self similarities I &mdash removing corner squares. Image Box fractal3.PNG Self similarities II &mdash keeping corner squares. gallery File Box or Vicsek Fractal 4 iterations.svg 550px thumb center Four iterations of the saltire form of the fractal top and the cross form of the fractal bottom . References reflist See also Cross crosslet List of fractals by Hausdorff dimension Sierpinski carpet Sierpinski triangle Category Fractals fr Fractale de Vicsek ... more details
Unreferenced date May 2009 Infobox Software name Ultra Fractal logo Image Ultra fractal logo.jpg 270px screenshot Image Ultra fractal screenshot.jpg 300px caption Ultra Fractal 4 on Windows XP author Frederik Slijkerman developer released May 2006 latest release version latest release date latest preview version latest preview date operating system Windows platform language English language English , German language German , Spanish language Spanish genre Fractal Renderer license Proprietary software Proprietary website http www.ultrafractal.com www.ultrafractal.com Ultra Fractal is a fractal generation and rendering Graphic art software software application . The program works using a similar paradigm to Photoshop , allowing multiple layers to be combined using Blend modes layer blending modes , Image warping transformations and custom fractal formula s. Fractal formulas, coloring algorithm s and transformations may be written by users and a large number of such formula Computer file file s are available in a public formula database . Fractals may be Cut, copy, and paste copied from the interface and pasted as plain text into an email , there is a busy Electronic mailing list mailing ... MDI . The software calculates statistic s about the fractal that is being previewed. Other features ... calculations and a detailed help file. Version 4 added support for animation s and improved Fractal flame flame fractal rendering. UltraFractal is Software industry Commercial commercial software , but an evaluation ... thumb right Example of a multi layered fractal made with Ultrafractal See also Fractal generating software Fractal art Fractint Apophysis software Apophysis Sterling program Sterling External links http www.ultrafractal.com Ultra Fractal http formulas.ultrafractal.com UF Formula Database http ultrafractalwiki.fractalforums.com Main Page Ultra Fractal Wiki Category Computer art Category Graphics software graphics software stub ru Ultra Fractal ... more details
Image Fractal antenna patent.gif thumb An example of a fractal antenna a space filling curve called a Minkowski ... array fractal antenna A fractal antenna is an Antenna radio antenna that uses a fractal , Self similarity ... total surface area or volume. Such fractal antennas are also referred to as multilevel and space filling ..., ref name r1 Nathan Cohen 2002 Fractal antennas and fractal resonators US Patent 6452553 ref or iterations . For this reason, fractal antennas are very compact, are multiband or wideband, and have useful applications in cellular telephone and microwave communications. A good example of a fractal antenna as a spacefilling curve is in the form of a shrunken fractal helix. ref name r2 http classes.yale.edu ..., each line of copper is just a small fraction of a wavelength. A fractal antenna s response differs .... This makes the fractal antenna an excellent design for wideband and multiband applications. Log periodic antennas and fractals The first fractal antennas were, in fact, fractal arrays , with fractal arrangements of antenna elements, and not recognized initially as having self similarity ... and DuHamel , that are such fractal arrays. They are a common form used in TV antennas, and are arrow head in shape. Fractal element antennas and performance Antenna elements as opposed to antenna arrays ... http www.fractenna.com nca cohen bio.html Fractal Antenna Systems, Inc Bot generated title ref then a professor at Boston University , starting in 1988. Cohen s efforts with a variety of fractal antenna designs were first published in 1995 thus the first scientific publication on fractal antennas , and a number ..., for example . Most allusions to fractal antennas make reference to these fractal element antennas . Many fractal element antennas use the fractal structure as a virtual combination of capacitors ... and adjusted by choosing the proper fractal design. Electrical resonances may not be directly related to a particular scale size of the fractal antenna structure. The physical size of the antenna is unrelated ... more details
Image ButterflyPhoenixDoubleNova wing zcode small.png right thumb 256px A PhonexDoubleNova fractal, rendered using five Clarify date April 2010 layers in UltraFractal . Image NovaFractal.png right thumb 256px A nova fractal with default Clarify date April 2010 parameters. Image NovaFractal relaxation.real 2.0.png right thumb 256px A nova fractal with Re R 2.0. Image NovaFractal relaxation.real 3.0.png right thumb 256px A nova fractal with Re R 3.0. Image NovaMaster coral romanesqueo.png right thumb 256px A 129804.49 times magnification at the point 0.43608549343268, 0.102470623996602 on the novaMandelbrot fractal with start value math z 0 9.0, 0.0 math , exponent math p 3.0, 0.0 math and relaxation math R 2.9, 0.0 math . Nova fractal is a family of fractals related to the Newton fractal . Nova is a formula that is implemented in most Citation needed date April 2010 fractal art software. Formula The formula for novaMandelbrot Citation needed date April 2010 is a special case of the generalized Newton fractal math z mapsto z R frac z p 1 pz p 1 , math where math R math is said to be a relaxation constant and math p in mathbb C math . Note that this expression is equivalent to math z mapsto z R frac f f math for math f z p 1 math , which is exactly the formula describing Newton fractals for a specific math f math . Category Fractals geometry stub ca Fractal Nova es Fractal Nova ... more details
Fractal Glider is Paul McCosh , a psychedelic trance artist from Melbourne , Australia . Fractal Glider is noted for his original high energy sound, and for being representative of the Melbourne psychedelic trance scene. See Gormack Although primarily playing in Australia , Japan and New Zealand , McCosh also participated in multiple parties and festivals in countries such as Portugal , Sweden , Switzerland , the Netherlands , France and Belgium , including the Earthcore electronic music festival. See Wehner McCosh began composing trance music in 1995, prior to which he worked as a sound engineer. His debut album, Parasite was released on Boom Records Netherlands . The second album, Digital Mandala features several new tracks and a remix of Mezmorized . To promote the new album McCosh went on an international tour through Japan, France, Netherlands, Belgium, Switzerland , Portugal, Hungary and Austria in 2003. Fractal Glider has also released singles on 14 compilations on different labels worldwide. A new album is due out in 2005 on London based Glowing Flame Records . Along with Ozzy, another Australian artist, Paul McCosh formed the group Liquid. The music features a fusion of electronic ... 5894 . The first Liquid album is due out in early 2005. Fractal Glider was featured on the television ... html profile.asp?content Fractal Glider&tablename Acts . Discography Parasite Fractal Glider album ... Fractal Glider Website http www.doofcentral.com index.php?option content&task view&id 15&Itemid 25 An 2002 Interview with Fractal Glider http northernbeats.com modules.php?name News&file article&sid 41 A 9 2004 Interview with Liquid Fractal Glider & Ozzy http www2.abc.net.au arts soundsliketechno html profile.asp?content Fractal Glider&tablename Acts Sounds Link Techno Profile Fractal Glider http www.discogs.com artist Fractal Glider Fractal Glider profile on Discogs References Nick Gormack ... on the Earthcore Electronic Music Festival, its underground nature, and Fractal Glider s participation ... more details
Fractal compression is a lossy data compression lossy image compression method using fractal s. The method ... resemble other parts of the same image. Citation needed date August 2009 Fractal algorithms convert these parts into mathematical data called fractal codes which are used to recreate the encoded image. Fractal compression differs from pixel based compression schemes such as JPEG , GIF and MPEG since no pixels are saved. Once an image has been converted into fractal code, the image can be recreated .... Iterated Function Systems main Iterated function system Fractal image representation can be described ... f N S math So we see the IFS is a fractal representation of S . Extension to Grayscale IFS representation ... R 3. math Encoding A challenging problem of ongoing research in fractal image representation is how ... to do this efficiently. A simple approach ref cite news last Fischer first Y. title Fractal ... blocks is why fractal encoding is much slower than for example discrete cosine transform DCT and wavelet based image representations. Features With fractal compression, encoding is extremely computationally ... is archived for distribution from disk storage or file downloads fractal compression becomes more ... ref At common compression ratios, up to about 50 1, Fractal compression provides similar results ... year 2005 location pages 560 569 url doi id isbn 012620862X ref At high compression ratios fractal ... fractal. ref have been achieved with acceptable results. Fractal video compression ratios of 25 1 ... ?aModele afficheN&cpsidt 1572685 Fractal encoding of video sequences ref Compression efficiency increases ... independence and fractal scaling An inherent feature of fractal compression is that images become resolution ... article on fractal compression resolution independence ref after being converted to fractal code ... scaling property of a fractal is known as fractal scaling . Fractal interpolation The resolution independence of a fractal encoded image can be used to increase the display resolution of an image ... more details
In geometry , and less formally, in most fractal art software, Fact date June 2008 the fractal lake of an orbits or Fractal Generating fractals escape time fractal , is the part of the complex plane for which the Orbit dynamics orbit a sequence of complex number s that is generated by iteration iterating a given function does not escape from the unit circle . Fact date June 2008 The lake may be Connectedness connected or Disjoint sets disjoint , and it may also have zero area . Orbits that are initialized inside the lake are either eventually captured by zero, captured by another point inside the unit circle, or may Oscillation oscillate through a set of finite values indefinitely without ever converging to a fixed point. These points are described as being Inside the lake. Inside points are often detected for the purposes of using a different coloring method, in fractal rendering software ref http spanky.triumf.ca WWW fractint color params.html Inside Outside coloring in Fractint ref By this definition, the points of the Mandelbrot set form a fractal lake , which is why the Mandelbrot set is also sometimes known as the Mandelbrot Lake ref http hpux.cs.utah.edu hppd cgi bin wwwtar? hpux X11 Misc xmfract 1.4 xmfract 1.4 hppa 10.10.depot.gz xmfract xmfract RUN opt xmfract bin help help.164 text WWWTar Query Bot generated title ref , or the lake of the Mandelbrot Fractal . Many complex valued functions with an attractor at the origin define a fractal when this aspect of their orbits behavior is categorized. Some of the orbits are attracted to the origin some are periodic some are attracted to other attractors, including possibly an attractor at infinity. For a given function there is a Julia set Julia fractal Mandelbrot set Relationship with Julia sets for each point on the complex plane. The Julia sets that correspond to points inside the Mandelbrot set are Connected space ... Mandelbrot set Julia set Nova fractal Filled Julia set Connectedness locus Lakes of Wada Notes references ... more details
Image Animated fractal mountain.gif thumb 300px A fractal landscape is a surface generated using a stochastic algorithm designed to produce fractal behaviour that mimics the appearance of natural terrain. In other words, the result of the procedure is not a deterministic fractal surface, but rather a random surface that exhibits fractal behaviour. ref cite web url http www.fractal landscapes.co.uk maths.html title The Fractal Geometry of Nature ref Many natural phenomena exhibit some form of statistical self similarity that can be modeled by fractal surfaces. ref name Cham Advances in multimedia ... of surfaces, and the use of almost self similar fractal patterns can help create natural looking ... Brownian motion was first proposed by Beno t Mandelbrot . ref Dynamics of Fractal Surfaces ... the overall fractal behavior of such a surface, in the interests of producing a more convincing landscape ... thumb right 250px An example of a fractal landscape Whether or not natural landscape s behave in a generally fractal matter has been the subject of some research. Technically speaking, any surface in three dimensional space has a topological dimension of 2, and therefore any fractal surface ... the overall fractal dimension of a real landscape can result in measures of negative fractal dimension, or of fractal dimension above 3. In particular, many studies of natural phenomena, even those commonly thought to exhibit fractal behaviour, do not in fact do so over more than a few orders of magnitude. For instance, Richardson s examination of the western coastline of Britain showed fractal ... place to place, so for example sandy beaches don t exhibit the same fractal properties as mountain ranges. A fractal function, however, is statistically stationary, meaning that its bulk statistical ... to modulate fractal behaviour spatially. Additionally real landscapes have very few natural minima most of these are lakes , whereas a fractal function has as many minima as maxima, on average. Real ... more details
Orphan date February 2009 Infobox Company company name Fractal Analytics company type Incorporation business Incorporated company logo Deleted image removed Image Fractal analytics.jpg foundation 2000 ... general overview Fractal Analytics is a provider of predictive analytics and Decision ... , retail and telecommunication industries. History Fractal Analytics is a provider of Business analytics ... creates a forward looking view of the client s business potential and risk. Fractal was started in 2000 ... and Fractal is currently run by Srikanth, Pranay and Nirmal. Five founders own about 40 of the firm ... since 2006. Business lines Fractal provides solutions for Customer acquisition management customer ... selling . Fractal s solutions are categorized under the following business lines CRM Analytics, Marketing ... www.efytimes.com efytimes 23085 news.htm Cranes, Fractal To Jointly Develop Predicta Bot generated ... Infotech Software Cranes Software in deal with Fractal Analytics for Predicta articleshow 2580946.cms Cranes Software in deal with Fractal Analytics for Predicta Software Infotech ... c.php?leftnm 10&autono 305941 Cranes to partner Fractal Analytics Bot generated title ref The F Metrics ... credit worthiness of consumers. ref http www.moneycontrol.com india news press news fractal analytics launches fmetrics 296998 Moneycontrol News Press News Fractal Analytics launches FMetrics Bot generated title ref , ref http www.tech2.com biz india news bfsi fractal analytics launches fmetrics 2702 0 Biztech India Fractal Analytics Launches FMetrics News on BFSI Bot generated title ref , ref http ... Fractal Analytics Launches Risk Assessment Product ... conversations Global Presence Fractal has worked with clients in the United States , Japan , Korea , Taiwan ... links http www.fractalanalytics.com Fractal Analytics website Co founder Ramakrishna Reddy s interview ... at Thinkingstreet.com on Fractal Analytics and the future of business analytics in India http www.thinkingstreet.com ... more details
Image Julian fractal.jpg thumb right 300px A piece of fractal art generated in Apophysis software Apophysis . Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and Algorithmic composition media . Fractal art is usually created indirectly with the assistance of fractal generating software , iterating through three phases setting parameters of appropriate fractal software executing the possibly lengthy ... in The Fractal Art Manifesto, Fractal Art is a subclass of two dimensional visual art, and is in many .... Fractal images typically are manifested as prints, bringing Fractal Artists into the company ... it is not. According to Mitchell, fractal art is not computerized art, lacking in rules, unpredictable, nor something that any person with access to a computer can do well. Instead, fractal art is expressive, creative, and requires input, effort, and intelligence. Most importantly, fractal art is simply that which is created by Fractal Artists ART. Fractal art comes from uses fractal designs. Fractals ... www.merriam webster.com dictionary fractal ref There are many different kinds of fractal images and can ... , a triangle the Sierpinski triangle , or a cube the Menger sponge . The first fractal figures invented .... Fractal terrains generated by random fractal processes. ref https www.fractalus.com fractal art ... choosing good looking specimens in a set of random variations of a fractal artwork and producing ... in the Electric Sheep project, where people use fractal flame s rendered with distributed computing ..., community created piece of art. Landscapes The first fractal image that was intended to be a work of art ... www.springerlink.com content p5p15267t7l11h07 Wondering angels of Fractal arts External links NoMoreLinks .... NoMoreLinks dmoz Science Math Chaos and Fractals Fractal art Fractal Art http commons.wikimedia.org ... http commons.wikimedia.org wiki Fractal Fractals in wikimedia Category Fractals Category Computer ... more details
Unreferenced date December 2009 about a two dimensional fractal in mathematics T square disambiguation In mathematics , the T square is a two dimensional fractal . As all two dimensional fractals, it has a boundary of infinite length bounding a finite area. Its name follows from that for a T square . Image T Square fractal evolution .png T square, evolution in six steps. br clear all Algorithmic description It can be generated from using this algorithm Image 1 Start with a square. Subtract a square half the original length and width one quarter the area from the center. Image 2 Start with the previous image. Scale down a copy to one half the original length and width. From each of the quadrants of Image 1, subtract the copy of the image. Images 3 6 Repeat step 2. Image T Square fractal 8 iterations .png thumb 256px T square . The method of creation is rather similar to the ones used to create a Koch snowflake or a Sierpinski triangle . Properties T square has a fractal dimension of ln 4 ln 2 2. The black surface extent is almost everywhere in the bigger square, for, once a point has been darkened, it remains black for every other iteration however some points remain white. The fractal dimension of the boundary equals math textstyle frac log 3 log 2 1.5849... math . See also List of fractals by Hausdorff dimension Sierpinski carpet DEFAULTSORT T Square Fractal Category Fractals bs T linijar fraktal hr T ravnalo fraktal sh T ravnalo fraktal ... more details
Orphan date September 2010 Userspace draft source ArticleWizard date August 2010 NGO Fractal is a non governmental organisation from Serbia that works on improving communication and cooperation of people from different backgrounds. It is a think tank organisation that engages itself in the discussion of issues such as security, Serb Albanian dialogues, energy, economy, self advocacy and social political problems one of its aims being to help raise awareness about such topics worldwide. NGO Fractal is member of EPLO European Peacebuilding Liasion Office ref http www.eplo.org index.php?id 45 ref , making it an internationally recognised non governmental organisation whose origins are from Serbia. Background NGO Fractal was founded by twelve people of different educational and professional backgrounds, and its current chairman is Filip Pavlovi . It has been involved in numerous projects, most famous being Project Enclavia ref http www.borba.rs content view 9846 123 ref which concentrates on reintegrating the alienated Serbian population into everyday life in Kosovo. References See http en.wikipedia.org wiki Wikipedia Footnotes on how to create references using ref ref tags which will then appear here automatically Reflist External links http www.eplo.org index.php?id 186 EPLO s website http ngofractal.org Fractal s website http www.borba.rs content view 9846 123 Article about one of Fractal s projects in Borba newspaper http www.b92.net info vesti index.php?yyyy 2007&mm 06&dd 07&nav category 12&nav id 250326 Article on Fractal s Kosovo project in B92 news DEFAULTSORT Ngo Fractal Category Non governmental organizations based in Serbia ... more details
Image KochFlake.svg thumb 140px The first four iteration s of the Koch snowflake In fractal geometry , the fractal dimension , D , is a statistical quantity that gives an indication of how completely a fractal ... definitions of fractal dimension. The most important theoretical fractal dimensions are the Fractal ... law function of the box size. Fractal dimension is estimated as the exponent of such power law ... these dimensions do coincide, in general they are not equivalent. One non trivial example is the fractal ... of an infinite number of segments joined at different angles. The fractal dimension of a curve can be explained intuitively thinking of a fractal line as an object too big to be a one dimensional object ... in a sense by the fractal dimension, which is a number between one and two. Specific definitions File ... ed http www.vanderbilt.edu AnS psychology cogsci chaos workshop Fractals.html Fractals & the Fractal Dimension Bot generated title ref There are two main approaches to generate a fractal structure. One ... of fractal structures See figure 1 . If we take an object with linear size equal to 1 residing in Euclidean ... equation to fractal structure, we can get the dimension of fractal structure which is more or less ... of linear size needed to cover the whole structure. For instance, the fractal dimension of the Sierpinski ... used to generate a representation of the fractal or attractor, and g sub sub is the number ... behaviour is occurring in different parts of the attractor. Estimating the fractal dimension of real world data The fractal dimension measures, described above, are derived from fractals which are formally defined. However, organisms and real world phenomena exhibit fractal properties see Fractal In nature Fractals in nature , so it can often be useful to characterise the fractal dimension of a set of Sample statistics sampled data. The fractal dimension measures cannot be derived exactly but must ... author B. Dubuc, J. F. Quiniou, C. Roques Carmes, C. Tricot, and S. W. Zucker title Evaluating the fractal ... more details
Image Lyapunov fractal AB.png thumb Standard Lyapunov logistic fractal with iteration sequence AB, in the region 2, 4 2, 4 . Image Lyapunov fractal AABAB.png thumb Generalized Lyapunov logistic fractal with iteration sequence AABAB, in the region 2, 4 2, 4 . Image lyapunov fractal.png thumb Generalized Lyapunov logistic fractal with iteration sequence BBBBBBAAAAAA, in the growth parameter region A,B in 3.4, 4.0 2.5, 3.4 , known as Zircon Zity . In mathematics , Lyapunov fractals also known as Markus Lyapunov fractals are bifurcational fractal s derived from an extension of the logistic map in which the degree of the growth of the population, r , periodically switches between two values A and B . A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour measured using the Lyapunov exponent math lambda math in the a &minus b plane for a given periodic sequence of a s and b s. In the images, yellow corresponds to math lambda 0 math stability , and blue corresponds to math lambda 0 math chaos . Properties Lyapunov fractals are generally drawn for values of A and B in the interval math 0,4 math . For larger values, the interval 0,1 is no longer stable, and the sequence is likely to be attracted by infinity, although convergent cycles of finite values continue to exist for some parameters. For all iteration sequences, the diagonal a b is always the same as for the standard one parameter logistic function. The sequence is usually started at the value 0.5, which is a critical point mathematics critical point of the iterative function. The other even ... to changes in the fractal, as some branches get covered by others notice for instance how the Lyapunov fractal for the iteration sequence AB is not perfectly symmetric with respect to a and b . Algorithm for generating Lyapunov fractals An algorithm , for computing the fractal is summarized as follows ... Fractale de Lyapunov ja pt Fractal de Lyapunov ru sl Fraktal Ljapunova ... more details
Infobox Album See Wikipedia WikiProject Albums Name Fractal Possession Type studio Artist Abigor Cover Released May 2, 2007 small EU small br June 5, 2007 small USA small Recorded Genre Black metal , industrial metal Length 52 44 Label End All Life Productions small EU small br Season Of Mist small USA small Producer Reviews Chronicles of Chaos webzine Chronicles of Chaos rating 6.5 10 http www.chroniclesofchaos.com reviews albums 2 4755 abigor fractal possession.aspx link Metal Temple rating 5 10 ref name metaltemple cite web url http www.metal temple.com site catalogues entry reviews cd 3 a 2 abigor fractal.htm work Metal Temple author Yiannis Doukas title Album Abigor, Fractal Possession, End All Life Productions date September 6, 2007 accessdate March 8, 2010 ref Last album Satanized br 2001 This album Fractal Possession br 2007 Next album Time Is the Sulphur in the Veins of the Saint br 2010 Fractal Possession is the seventh studio album by Austrians Austrian black metal band Abigor . It was released worldwide in 2007. Track listing tracklist all lyrics AR, PK all music PK, TT title1 Warning length1 1 53 title2 Project Shadow length2 5 38 title3 Cold Void Choir length3 6 13 title4 Lair of Infinite Desperation length4 6 07 title5 3D Blasphemy length5 5 43 title6 The Fire Syndrome length6 5 51 title7 Injection Satan length7 4 25 title8 Liberty Rises a Diagonal Flame length8 5 05 title9 Vapourized Tears length9 5 10 title10 Heaven Unveiled length10 6 39 Credits A.R. Arthur Rosar Vocals P.K. Virus 666, Peter Kubik Guitars, Bass T.T. Thomas Tannenberger Drums, Guitars External links http www.metal archives.com release.php?id 147277 Encyclopaedia Metallum Abigor Fractal Possession Allmusic class album id r1067753 pure url yes Allmusic Abigor Fractal Possession References reflist Abigor Category 2007 albums Category Abigor albums Category Season of Mist albums 2000s black metal album stub pl Fractal Possession ... more details
Fractal Design was a US software company, originally known as Fractal Software and founded in 1985. ref name MarkZimmer cite web url http www.linkedin.com pub mark zimmer 9 235 57a title Mark Zimmer publisher Mark Zimmer accessdate 2010 09 13 ref It merged into MetaCreations in 1997 ref name MetaHistory cite web url http www.macworld.com article 15550 1999 12 15metacreations.html title MetaCreation s Puzzling Move publisher Stephen Beale, MacWorld.com, December 15, 1999 accessdate 2010 09 13 ref . It was initially known as Fractal Technology, and produced several best selling creative software packages for the PC and Macintosh platforms. Its initial success was Fractal Painter, a natural media drawing program released in 1990. It acquired Ray Dream Software in 1996. In 1997, it was merged into MetaCreations. The products in its portfolio were later sold off to other major software producers including Corel and Microsoft . Fractal Design s original products included Corel Painter Painter , a natural media painting program, currently available from Corel Poser , a 3D modeling program, currently available from Smith Micro Software Dabbler , a basic natural media program. Sketcher , a basic grayscale program. Detailer, a 3D painting program, later known as Painter 3D Fractal Design also purchased and released Creature House Expression from Creature House software. References reflist US software company stub Category Software companies of the United States ... more details
, fractal cosmology is a set of minority cosmology cosmological theories which state that the distribution of matter in the Universe , or the structure of the universe itself, is fractal . More ... . A central issue in this field is the fractal dimension of the Universe or of matter distribution ... of science , so some varieties of fractal cosmology are solidly in the realm of scientific theories ... of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, ref cite journal author Pieronero, L. year 1987 title The Fractal Structure of the Universe Correlations of Galaxies ... grew larger. Pietronero argues that the universe shows a definite fractal aspect, over a fairly wide range of scale, with a fractal dimension of about 2. ref cite journal author Joyce, M. Labini, F.S. ... the large scale structure in the universe is fractal out to at least 100 Mpc h. The paper asserts that the team ... based solely on gravity. Their analysis shows the fractal dimension of the arrangement of galaxies ... of luminous red galaxy luminous red galaxies in the Sloane survey calculated the fractal dimension ... confirm that the fractal dimension is 2 out to roughly 20 Mpc h . ref cite journal author Hogg, David ... into bubble universes, making the universe fractal on the very largest scales. Alan Guth Alan Guth ... a large number of different cosmological theories exhibiting fractal properties have been proposed ... hep th 0511260 doi pmid pmc ref are fractal at the opposite extreme, in the realm of the ultra small near the Planck scale . These recent theories of quantum gravity describe a fractal structure for spacetime ... scales. French astronomer Laurent Nottale first suggested the fractal nature of spacetime in a paper ... 20 pages 4899 4936 url doi pmid pmc ref and published a book on the subject of Fractal Space Time in 1993. ref cite book author Nottale, Laurent year 1993 title Fractal Space time and Microphysics .... Both approaches suggest that the fabric of space itself is fractal, however. Publications ... more details
Unreferenced date September 2010 The fractal transform is a technique invented by Michael Barnsley et al. to perform lossy data compression lossy image compression . This first practical fractal compression system for digital images resembles a vector quantization system using the image itself as the codebook. Fractal transform compression Start with a digital image A sub 1 sub . Downsample it by a factor of 2 to produce image A sub 2 sub . Now, for each block B sub 1 sub of 4x4 pixels in A sub 1 sub , find the corresponding block B sub 2 sub in A sub 2 sub most similar to B sub 1 sub , and then find the grayscale or RGB color space RGB offset and gain from A sub 2 sub to B sub 2 sub . For each destination block, output the positions of the source blocks and the color offsets and gains. Fractal transform decompression Starting with an empty destination image A sub 1 sub , repeat the following algorithm several times Downsample A sub 1 sub down by a factor of 2 to produce image A sub 2 sub . Then copy blocks from A sub 2 sub to A sub 1 sub as directed by the compressed data, multiplying by the respective gains and adding the respective color offsets. This algorithm is guaranteed to converge to an image, and it should appear similar to the original image. In fact, a slight modification of the decompressor to run at block sizes larger than 4x4 pixels produces a method of stretching images without causing the blockiness or blurriness of traditional linear resampling algorithm s. Patents Michael Barnsley and friends own numerous patent s in the United States and elsewhere on what this article describes. These include U.S. Patents 4,941,193, 5,065,447, 5,384,867, 5,416,856, and 5,430,812. These patents have hindered widespread adoption of the fractal transform in image coding. If you live in United States or other country with software patent s, you can do fractal compression ... Fractal Transform Category Fractals sv Fraktaltransformation ... more details
, math k 1,.., operatorname deg p math . In this way the Newton fractal is similar to the Mandelbrot ... sets. It is this property that causes the fractal structure of the Julia set when the degree of the polynomial ... Raphson author Simon Tatham ref . The special choice math a 1 math corresponds to the Newton fractal ... still exhibits a fractal structure in the sense of Julia set . If math p math is a polynomial of degree ... of radius math n math centered at math n math . More generally, Newton s fractal is a special case of a Julia set . gallery Image FRACT008.png Newton fractal for three degree 3 roots math p z z 3 1 math , coloured by number of iterations required Image Newtroot 1 0 0 m1.png Newton fractal for three degree 3 roots math p z z 3 1 math , coloured by root reached Image Newton z3 2z 2.png Newton fractal ... Newton fractal for math x 8 15x 4 16 math Image Newtroot 1 0 m3i m5m2i 3 1.png Newton fractal for math ... Image timelapse4.jpg Newton fractal for math p z sin z math , coloured by root reached, shaded by number of iterations required Image Sin x detail.png Another Newton fractal for math sin x math Image Mnfrac1.png Generalized Newton fractal for math p z z 3 1 math , math a 0.5. math The colour was chosen based on the argument after 40 iterations. Image Mnfrac2.png Generalized Newton fractal for math p z z 2 1 math , math a 1 i. math Image Mnfrac3.png Generalized Newton fractal for math p z z 3 1 math , math a 2. math Image Mnfrac4.png Generalized Newton fractal for math p z z 4 3i 1 math , math a 2.1. math gallery See also Julia set Mandelbrot set Nova fractal References reflist http www.math.sunysb.edu ... 1 Newton s Method as a Dynamical System by Johannes Rueckert Commons Newton fractal Newton fractal ... more details
image Rauzy fractal.png thumb 300px Rauzy fractal In mathematics, the Rauzy fractal is a fractal set associated to the Tribonacci String substitution substitution math s 1 12, s 2 13, s 3 1 , math It has been studied in 1981 by G rard Rauzy ref http archive.numdam.org ARCHIVE BSMF BSMF 1982 110 BSMF 1982 110 147 0 BSMF 1982 110 147 0.pdf G. Rauzy, Nombres alg briques et substitutions, Bulletin de la Soci t Math matique de France, 110 147 178, 1982 ref , with the idea of generalizing the dynamic properties of the Fibonacci word Fibonacci morphism . That fractal set can be generalized to other maps on a 3 letter alphabet, generating other fractal sets with interesting properties periodic tessallation tiling of the plane, self similarity in three homothety homothetic parts.. Definitions The infinite tribonacci word is a Word mathematics word constructed by applying iteratively the Tribonacci map math s 1 12 math , math s 2 13 math , math s 3 1 math . Starting from 1, the Tribonacci words are math t 0 1 math math t 1 12 math math t 2 1213 math math t 3 1213121 math math t 4 1213121121312 math We can show that, for math n 2 math , math t n t n 1 t n 2 t n 3 math , hence the name Tribonacci number Tribonacci . image Rauzy fractal construction.png thumb 300px Construction Let s consider, now, the space math R 3 math with cartesian coordinates x,y,z . The Rauzy fractal is constructed this way 1 Interpret the sequence of letters of the infinite Tribonacci word as a sequence of unitary Vector mathematics and physics vectors of the space, with the following rules 1 direction x, 2 direction ... math . Its boundary is fractal, and the Hausdorff dimension of this boundary equals 1.0933. Solution ..., Fronti re du fractal de Rauzy et syst me de num ration complexe, Acta Arithmetica, 2000 ref . Variants ... condition apparently always verified , one can construct a similar set called Rauzy fractal of the map ... references See also List of fractals Tribonacci number External links Commons Category Fractalfractal ... more details
orphan date March 2010 Infobox Album See Wikipedia WikiProject Albums Name Fractal Type EP Artist Skyfire band Skyfire Cover Skyfire Fractal EP Album Art.jpg Released July 6, 2009 Recorded 2005 2009 at Powernest Studios Genre Melodic death metal Length 21 55 Label Pivotal Rockordings Producer Last album Haunted By Shadows br 2003 This album Fractal br 2009 Next album Fractal is a digital only Extended play EP by Swedish heavy metal music metal band Skyfire band Skyfire . It was made available for music download digital download on July 6, 2009. The EP contains four songs, which were recorded between the release of Spectral album Spectral in 2004 and their album Esoteric album Esoteric released in September 2009. ref name blabbermouthrelease cite web url http www.roadrunnerrecords.com blabbermouth.net news.aspx?mode Article&newsitemID 120402 title Skyfire Digital Only EP Details Revealed date May 19, 2009 publisher blabbermouth.net accessdate 2009 07 08 ref The EP features the debut of two new members guitarist Johan Reinholdz and Joakim Karlsson. It contains three tracks independent of the full length and the self titled track from their album. This track was previewed on their official MySpace page and was made available for download. ref name blabbermouthrelease Track listing The Land of the Wolves 6 03 Bereaved in Denial 4 37 The Transgressor Within 6 32 Esoteric 4 43 Personnel Band members Joakim Karlsson singing vocals Martin Hanner bass guitar , Keyboard instrument keyboards Andreas Edlund electric guitar guitars , keyboards Johan Reinholdz guitars Joakim Jonsson drum kit drums Production Recorded, mixed and mastered at Powernest Studios with the exception of the track Esoteric , which was mixed and mastered by Jonas Kjellgren Vocals on all tracks produced by guitarist Patrik Persson The Forsaken References reflist Category 2009 EPs Category Skyfire albums 2000s death metal album stub ... more details
Image Electricsheep 14156.jpg thumb 300px A fractal flame created by the Electric Sheep . Image Swirly belt444.jpg thumb 300px Fractal flame created in Apophysis software Apophysis . Fractal flames are a member of the iterated function system class ref Mitchell Whitelaw 2004 . Metacreation Art and Artificial Life . MIT Press. pp 155. ref of fractal s created by Scott Draves in 1992. ref name apophysis cite web url http apophysis.wikispaces.com title Information about Apophysis software accessdate 2008 03 11 ref Draves open source code was later ported into Adobe After Effects graphics software ref Chris Gehman and Steve Reinke 2005 . The Sharpest Point Animation at the End of Cinema . YYZ Books. pp 269. ref and translated into the Apophysis software Apophysis fractal flame editor. ref name apophysis Fractal flames differ from ordinary iterated function systems in three ways Nonlinear functions are Iteration iterated instead of Affine transformation affine transforms . Log density display instead of linear or binary a form of tone mapping Colour by structure i.e. by the recursive path taken instead of monochrome or by density. The tone mapping and coloring are designed to display as much of the detail of the fractal as possible, which generally results in a more aesthetically pleasing ... V sub k sub . Draves suggests ref name dravespdf PDFlink http flam3.com flame.pdf The Fractal ... x y frequency max source but this would make some parts of the fractal lose detail, which is undesirable. ref name dravespdf See also Apophysis software Apophysis , an open source fractal flame editor for Microsoft Windows. Electric Sheep , a screen saver created by the inventor of fractal flames which ... manipulation program that can generate fractal flames. References references External links http code.google.com p flam3 Documentation and Source Code http flam3.com Project Home Page commonscat Fractal flames DEFAULTSORT Fractal Flame Category Fractals ... more details
Encyclopedia
top
