that models the surface of a mountain animation thumb right Further Fractal art Fractal patterns ...for the popular art form Fractal art Spoken Wikipedia Fractal.ogg 2005 06 16 anchor Mandelbrot zooms ... the full set. A fractal is a mathematical Set mathematics set that has a fractal dimension that usually ... A fractal set is one for which the fractal Hausdorff Besicovitch dimension strictly exceeds the topological ... author Mandelbrot,Beno t B. title The fractal geometry of nature url http books.google.com books?id ... name Falconer ref name patterns ref name vicsek The definition of fractal goes beyond self similarity ... fractal curve can be perceived of as winding through space differently from an ordinary line, still being a topological dimension 1 dimensional line yet having a fractal dimension indicating it also resembles a surface. ref name Mandelbrot Chaos rp 48 ref name Mandelbrot1983 rp 15 The mathematical ... functions in the 19th century, and on to the coining of the word wikt fractalfractal in the 20th ... in the 21st century. ref name classics ref name MacTutor The term fractal was first used by mathematician ... broken or fractured , and used it to extend the concept of theoretical fractional fractal dimension ... There is some disagreement amongst authorities about how the concept of a fractal should be formally ... iterated , and detailed mathematical constructs having fractal dimensions, of which many List of fractals ... describe processes in time. ref name Gouyet ref name vicsek ref name time series Fractal patterns ... and fractals in art art . ref name novel ref name African art ref name fractal painting Introduction The word fractal often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. The mathematical ... feature that can be understood without mathematical background Having a fractional or fractal dimension greater than its topological dimension, for instance, refers to how a fractal scales compared ... 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 fractalsurface, 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 ... and even the overall fractal behavior of such a surface, in the interests of producing a more convincing ... books.google.com books?id IRy3l6zUGE4C&pg PA297&dq 22fractal surface 22&hl en&ei UxTzTMHsN8PysgbP8pmGCw ... ref Moreover, variations in surface texture provide important visual cues to the orientation and slopes of surfaces, and the use of almost self similar fractal patterns can help create natural looking ... 22fractal surface 22&hl en&ei xSDzTKThHsX4sgb7qMSCCw&sa X&oi book result&ct result&resnum 6&ved 0CD4Q6AEwBTgU ... via fractional Brownian motion was first proposed by Beno t Mandelbrot . ref Dynamics of Fractal Surfaces ... FractalLandscape.jpg thumb An example of a fractal landscape File Fractal terrain texture.jpg thumb Fractal terrain File BlueRidgePastures.jpg thumb Fractal pastures Whether or not natural landscape s behave in a generally fractal manner has been the subject of some research. Technically speaking, any surface in three dimensional space has a topological dimension of 2, and therefore any fractalsurface in three dimensional space has a Hausdorff dimension between 2 and 3. ref Lewis Lewis ref ... 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 ... more details
total surface area or volume. Such fractal antennas are also referred to as multilevel and space filling ...Image Fractal antenna patent.gif thumb An example of a fractal antenna a space filling curve called a Minkowski ... fractal antenna A fractal antenna is an Antenna radio antenna that uses a fractal , Self similarity ... name r1 Nathan Cohen 2002 Fractal antennas and fractal resonators US Patent 6452553 ref or iterations . For this reason, fractal antennas are very compact, 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 ... line of copper is just a small fraction of a wavelength. A fractal antenna s response differs markedly .... 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 ... , 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 ... 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 of patents have been issued from the 1995 filing priority of invention. Most allusions to fractal antennas make reference to these fractal element antennas . Many fractal element antennas use the fractal ... that it has many different resonances which can be chosen and adjusted by choosing the proper fractal design. Electrical resonances may not be directly related to a particular scale size of the fractal ... itself in the same way with fractal antennas. This complexity arises because the current on the structure ... more details
FWF Samuel Monnier d tail.jpg thumb A Fibonacci word fractal by Samuel Monnier 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 developed from the mid 1980s onwards. ref name fgad cite book title Fractal geometry in architecture and design last Bovill ... as icon s of fractal art. ref name hema cite book title The heart of mathematics an invitation to effective ... 2011 ref Fractal art is not drawn or painted by hand. It 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 calculation and evaluating the product. In some ... post processing. Non fractal imagery may also be integrated into the artwork. ref name mra Fractal art could not have developed without computers because of the calculation calculative .... ref http www.merriam webster.com dictionary fractalFractal Definition . Free Merriam Webster Dictionary. ref The Fractal Art Manifesto As stated by Kerry Mitchell in The Fractal Art Manifesto, ref name manif cite web url https www.fractalus.com info manifesto.htm title The Fractal Art Manifesto author Kerry Mitchell date work publisher accessdate 28 October 2011 ref Fractal Art is a subclass ... by skepticism upon its arrival. Fractal images typically are manifested as Printmaking prints , bringing fractal artists into the company of painters, photographers, and printmakers. Fractals ... embracing, bringing them into Fractal Art s digital realm. Generating fractals can be an artistic endeavor, a mathematical pursuit, or just a soothing diversion. However, Fractal Art is clearly distinguished ..., 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 ... 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
with fractal dimension 1.9 winds convolutedly through space very nearly like a surface. Similarly, a surface with fractal dimension of 2.1 fills space very much like an ordinary surface, but one with a fractal ... fractal coastline 200km.png alt1 Coastline of Britain measured using a 200 km scale caption1 small 11.5 x 200 2300 km small image2 britain fractal coastline 100km.png alt2 Coastline of Britain measured using a 100 km scale caption2 small 28 x 100 2800 km small image3 britain fractal coastline ... A fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern strictly speaking, a fractal pattern changes with the Scaling geometry scale at which it is measured ... of a pattern that tells how a fractal scales differently than the space it is embedded in a fractal .... ref cite book last Falconer first Kenneth title Fractal Geometry publisher Wiley location New ... last Vicsek first Tam s title Fractal growth phenomena publisher World Scientific location Singapore ... of that notion, the fractal dimension of a coastline quantifies how the number of scaled measuring ... There are several formal specific definitions mathematical definitions of fractal dimension ... is the fractal dimension of a Koch snowflake . It has a topological dimension of 1, but it is by no means ... is composed 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 detailed to be one ... fractal dimension, which in this case is a number between one and two. Introduction Anchor 32seg Image 32 segment fractal.jpg thumb right Figure 2. A 32 segment fractal iterated quadric fractal scaled ... fractal dimension for this fractal is log32 log8 1.67 its empirical fractal dimension from box counting analysis is 1 ref name empirical fractal dimension cite book page 95 author Karperien title Defining Microglial Morphology Form, Function, and Fractal Dimension publisher Charles Sturt University ... 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
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 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
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 is a fractal arising from a construction similar to that of the Sierpinski carpet . It has applications including as compact fractal antenna antennas , particularly in cellular phones. Construction 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 math textstyle frac log 5 log 3 math 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 . Properties The Vicsek fractal has the surprising property that it has .... The perimeter approaches infinity as n increases. The boundary of the Vicsek fractal is the Koch ... Image 3D Vicsek Fractal.gif thumb right 200px Animation of the 3D analogue of the Vicsek fractal third iteration There is a three dimensional analogue of the Vicsek fractal. It is constructed by subdividing ... 7 log 3 math 1.7712. Similarly to the two dimensional Vicsek fractal, this figure has zero volume. Each ... of Cross section geometry cross section s which yield the two dimensional Vicsek fractal. References ... 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 location United States, United Kingdom, Singapore, India num employees about 250 revenue Confidential industry Analytics , Knowledge process outsourcing Knowledge Process Outsourcing products Customer Lifecycle Management, CRM Analytics, Marketing Mix Management, Consumer Insight Analytics, Business ... Fractal Analytics Fractal Analytics is a provider of predictive analytics and Decision theory ... industries. History Fractal Analytics is a provider of Business analytics analytics ... s response to price changes and forecast business performance. Fractal is headquartered in San ... 50 of the firm, the rest is owned by investors. Fractal was started in 2000 by five founders Nirmal ... to other shareholders. Business lines Fractal provides solutions for Customer acquisition management ... cross selling . Fractal s solutions are categorized under the following business lines CRM Analytics ... 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 ... InfSecurityAug03 07FractalAnalyticsLaunchesRiskAssessmentProductforBanks.aspx Fractal Analytics ... surveillance listens in on web conversations Global Presence Fractal has worked with clients in the United ... and the United States External links http www.fractalanalytics.com Fractal Analytics website ... nuggets of data Financial Times CEO Srikanth Velamakanni s interview at Thinkingstreet.com on Fractal ... 12 08 interview with srikanth velamakanni ceo fractal analytics Interview Fractal ranked as the Top ... Fractal best KPO Black Book of Outsourcing recognizes Fractal Analytics as a top KPO globally for the second ... 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 Wikt finite 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 .... See also Mandelbrot set Julia set Nova fractal Filled Julia set Connectedness locus Lakes of Wada ... more details
. citation needed date November 2011 Fractal Glider has also released singles on 14 compilations on different labels worldwide. citation needed date November 2011 Fractal Glider appeared on the television ... as 2008 he was apparently still recording music. ref http www.myspace.com fractalglider Fractal Glider MySpace page ref Discography Parasite Fractal Glider album Parasite Boom Records 2002 Digital Mandala Boom Records 2003 External links http www.allmusic.com artist fractal glider p832994 Fractal Glider at Allmusic http www.last.fm music Fractal Glider Fractal Glider at last.fm http www.discogs.com artist Fractal Glider Fractal Glider profile on Discogs http www.doofcentral.com index.php?option ... Electronic Music Festival, its underground nature, and Fractal Glider s participation therein ... more details
Fractal compression is a lossy compression method for digital image s, based on fractal s. The method ... 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. Iterated Function Systems main Iterated function system Fractal image representation can be described ... So we see the IFS is a fractal representation of S . Extension to Grayscale IFS representation ... Encoding A challenging problem of ongoing research in fractal image representation is how to choose ... to do this efficiently. A simple approach ref cite news last Fischer first Y. title Fractal Image Compression ... 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 ... for distribution from disk storage or file downloads fractal compression becomes more competitive ... ref At common compression ratios, up to about 50 1, Fractal compression provides similar results to Discrete ... year 2005 location pages 560 569 url doi id isbn 0 12 620862 X ref At high compression ratios fractal ... fractal. ref have been achieved with acceptable results. Fractal video compression ratios of 25 1 244 ... ?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. This is because ... 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. This process is also known as fractal interpolation . In fractal interpolation, an image is encoded into fractal codes via fractal compression, and subsequently decompressed at a higher resolution. The result ... 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 Defunct software companies of the United States ... more details
for Modelling graphics using fractals Fractal modeling Fractal analysis is assessing fractal characterisics of data . It consists of several methods to assign a fractal dimension and other fractal characteristics ... ref name heart cite doi 10.1113 jphysiol.2009.169219 ref , digital images ref Fractal Analysis of Digital ..., etc. Fractal analysis is now widely used in all areas of science ref cite journal title Fractals ... fractals.shtml issn 1793 6543 ref . An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal rather, other fractal characteristics essential characteristics have to be considered. ref name Mandelbrot1983 cite book author Beno t B. Mandelbrot title The fractal geometry of nature url http books.google.com ... 0716711865 ref Types of fractal analysis Several types of fractal analysis are done, including box counting , lacunarity lacunarity analysis , mass fractal dimension mass methods , and multifractal analysis ref name Mandelbrot1983 ref name time series . A common feature of all types of fractal analysis ... citations ref These can be acquired with various types of fractal generating software capable ... to render fractal art . Applications Applications of fractal analysis include ref cite web url ... 7172 2 ref Fractal landscape or Coast line complexity ref name Mandelbrot1983 ref name coastline ... in Proteins Algorithmic composition Generation of new music Fractal art Generation of various art ... and Fractal compression image compression col break urban growth ref name Chen2011 cite doi 10.1371 ... accessdate 2011 02 05 ref http fr.arxiv.org abs 0904.0780 Wave propagation in self similar fractal media Fractal in soil mechanics Soil studies ref name soil cite doi 10.1016 j.apgeog.2011.10.016 ref ... 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 ... more details
Orphan date September 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 Liaison 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
one source date March 2012 Infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name The Fractal Prince image image caption author Hannu Rajaniemi cover artist country UK language English series genre Science fiction novel publisher Victor Gollancz Ltd Gollancz release date 2012 media type Print Hardcover Hardback & Paperback pages 448 pp isbn Special BookSources 9780575088917 9780575088917 Hardback Special BookSources 9780575088924 9780575088924 The Fractal Prince is the second science fiction novel by Hannu Rajaniemi . It will be published in Britain by Victor Gollancz Ltd Gollancz in 2012, as well as by Tor Books Tor in the US. ref name upcoming4me http upcoming4.me media news book news item 9332 hannu rajaniemi the fractal prince cover art, release date, and preorder details Hannu Rajaniemi The Fractal Prince cover art, release date, and preorder details on Upcoming4.me ref Plot introduction On the edges of physical space a thief, helped by a sardonic ship, is trying to break into a Schrodinger box. He is doing the job for his patron, and owner of the ship, Mieli. In the box is his freedom. Or not. The box is protected by codes that twist logic and sanity. And the ship is under attack. The thief is nearly dead, the ship is being eaten alive. Jean de Flambeur is running out of time. All of him. And on earth, two sisters in a city of fast ones, shadow players and jinni contemplate a revolution. There are many more stories than can be told even in a thousand nights and one night, but these two stories will twist, and combine. And reality will spiral. ref name upcoming4me Bibliography The Fractal Prince , Hannu Rajaniemi Gollancz, 2012, ISBN 978 0 575 08891 7 paperback ISBN 978 0 575 08892 4 References reflist DEFAULTSORT Fractal Prince, The Category 2012 novels Category Novels by Hannu Rajaniemi Category 2010s science fiction novels fi Kvanttivaras ... more details
fractal is similar to the Mandelbrot set , and like other fractals it exhibits an intricate appearance ... for each of the Fatou sets. It is this property that causes the fractal structure of the Julia ... to the Newton fractal. The fixed points of this map are stable when math a math lies inside ... unstable, however the map still exhibits a fractal structure in the sense of Julia set . If math ... s fractal is a special case of a Julia set . gallery Image FRACT008.png Newton fractal for three ... 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 for math p z z 3 2z 2 math . Points in the red basins do not reach a root. Image Colored Newton Fractal 2.png Newton fractal for a 7th order polynomial, colored by root reached and shaded by rate of convergence. Image timelapse34.jpg Newton fractal for math x 8 15x 4 16 math Image Newtroot 1 0 m3i m5m2i 3 1.png Newton fractal for math p z z 5 3iz 3 5 2i z 2 3z ... 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 scott J. H. Hubbard ... System by Johannes Rueckert Commons Newton fractal Newton fractal Category Numerical analysis ... 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
, 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 a 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 ... shows a definite fractal aspect, over a fairly wide range of scale, with a fractal dimension ... is fractal out to at least 100 Mpc h. The paper asserts that the team has demonstrated that the most ... shows the fractal dimension of the arrangement of galaxies in the universe up to the range of 30 ... in the Sloane survey calculated the fractal dimension of galaxy distribution on a scales from 70 to 100 Mpc h at 3, consistent with homogeneity they also confirm that the fractal dimension is 2 ... which cause inflating patches of space to develop into bubble universes, making the universe fractal ..., however, quite a large number of different cosmological theories exhibiting fractal properties have ... pmc bibcode 2005hep.th...11260L 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 ... issue 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 ... of space itself is fractal, however. Publications The book Discovery of Cosmic Fractals ... Baryshev and Pekka Teerikorpi gives an overview of fractal cosmology, and recounts other milestones ... 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 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 Album ratings rev1 Chronicles of Chaos webzine Chronicles of Chaos rev1score rating 6.5 10 ref http www.chroniclesofchaos.com reviews albums 2 4755 abigor fractal possession.aspx Chronicles of Chaos review ref rev2 Metal Temple rev2score 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 Automatically generated by DASHBot 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 ... metal album stub pl Fractal Possession ... 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
A fractal globule is a proposed packing method used by cells to sequester DNA into a compact yet accessible structure that minimizes the probability of knot formation. ref name lieberman2009 cite doi 10.1126 science.1181369 ref ref name grosberg1993 cite doi 10.1209 0295 5075 23 5 012 ref ref name grosberg1988 cite doi 10.1051 jphys 0198800490120209500 ref A paper by a team of scientists from the University of Massachusetts Medical School and MIT Erez Lieberman Aiden , van Berkum et al ref name lieberman2009 2009 described Hi C, a method that probes the three dimensional architecture of whole genomes by coupling proximity based ligation with massively parallel sequencing. We constructed spatial proximity maps of the human genome with Hi C at a resolution of 1 megabase. These maps confirm the presence of chromosome territories and the spatial proximity of small, gene rich chromosomes. We identified an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome wide compartments. At the megabase scale, the chromatin conformation is consistent with a fractal globule , a knot free, polymer conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus. The fractal globule is distinct from the more commonly used globular equilibrium model. Our results demonstrate the power of Hi C to map the dynamic conformations of whole genomes. References Reflist Category DNA Category Fractals ... 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 ... Fractalfractal http www.dmg.tuwien.ac.at nfn Topological.pdf Topological properties of Rauzy fractals ... more details
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