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
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 Color 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 image. Algorithm The algorithm consists of two steps creating a histogram and then rendering the histogram ... V sub k sub . Draves suggests ref name dravespdf PDFlink http flam3.com flame.pdf The Fractal ... max source but this would make some parts of the fractal lose detail, which is undesirable. ref ... , an open source fractal flame editor for Microsoft Windows. Electric Sheep , a screen saver created by the inventor of fractal flames which renders and displays them with Distributed computing . GIMP , a free software , multi OS image manipulation program that can generate fractal flames. References references commons category Fractal flames DEFAULTSORT Fractal Flame Category Fractals ... more details
In mathematics , a fractal sequence is one that contains itself as a proper subsequence. An example is 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, ... If the first occurrence of each n is deleted, the remaining sequence is identical to the original. The process can be repeated indefinitely, so that actually, the original sequence contains not only one copy of itself, but rather, infinitely many. Definition The precise definition of fractal sequence depends on a preliminary definition a sequence x x sub n sub is an infinitive sequence if for every i, F1 x sub n sub i for infinitely many n. Let a i,j be the jth index n for which x sub n sub i. An infinitive sequence x is a fractal sequence if two additional conditions hold F2 if i 1 x sub n sub , then there exists m n such that i x sub m sub F3 if h i then for every j there is exactly one k such that a i,j a h,k a i,j 1 . According to F2 , the first occurrence of each i 1 in x must be preceded at least once by each of the numbers 1, 2, ..., i 1, and according to F3 , between consecutive occurrences of i in x, each h less than i occurs exactly once. Example Suppose is a positive irrational number. Let S the set of numbers c d , where c and d are positive integers and let c sub n sub d sub n sub be the sequence obtained by arranging the numbers in S in increasing order. The sequence c sub n sub is the signature of , and it is a fractal sequence. For example, the signature of the golden ratio i.e., 1 sqrt 5 2 begins with 1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, ... and the signature of 1 1 begins with 1, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, ... These are sequences OEIS2C A084532 and OEIS2C A084532 in the On Line Encyclopedia of Integer Sequences , where further examples from a variety of number theoretic and combinatorial settings ... OEIS2C A022447 OEIS2C A125158 OEIS2C A125159 OEIS2C A108712 References Clark Kimberling, Fractal ... more details
Infobox album See Wikipedia WikiProject Albums Name To the Extreme Type Album Artist Vanilla Ice Cover Vanilla Ice To the Extreme album cover .JPG Released August 28, 1990 Recorded 1989 1990 Genre Hip ..., Khayree, Darryl Williams Last album This album To the Extreme br 1990 Next album Mind Blowin br 1994 Misc Singles Name To the Extreme Type studio Single 1 Play That Funky Music Single 1 date April 25, 1990 Single 2 Ice Ice Baby Single 2 date July 2, 1990 Single 3 I Love You Single 3 date 1990 To the Extreme ... . Although reviews of the album were mixed, To the Extreme spent 16 weeks at the top of the Billboard ... version of To the Extreme under the title Hooked on Ichiban Records . ref cite web url Allmusic ... Winkle signed to SBK Records , who reissued Hooked under the title To the Extreme . The reissue contained ... Huey cite web url Allmusic class album id r28388 pure url yes title Review of To the Extreme accessdate ... Ice To The Extreme SBK journal Smash Hits publisher EMAP EMAP Metro issue 12 25 December 1990 page ... List Automatically Moved by DASHBot To the Extreme became the fastest selling hip hop music ... Billboard cite web url Allmusic class album id r28388 pure url yes title Charts and awards for To the Extreme ... ref To the Extreme was the best selling hip hop album up until that time. ref cite book last1 Perkins ... ref Reviews of To the Extreme were mixed. Entertainment Weekly reviewer Dom Lombardo gave the album ... title Review of To the Extreme accessdate 2009 02 13 last Udovitch first Mim date November 2, 1990 ... of To the Extreme accessdate 2009 03 07 last Christgau first Robert year 1990 publisher The Village ... 1 24 Track listing headline To the Extreme extra column Producer s total length 57 22 writing credits ... 1 09 Personnel The following people contributed on To the Extreme ref cite web url Allmusic class album id r28388 pure url yes title Credits for To the Extreme accessdate 2009 03 07 publisher Allmusic ... To The Extreme Category 1990 debut albums Category Vanilla Ice albums Category SBK Records albums pt ... more details
orphan date December 2007 tone date December 2007 Edward Soja uses the term fractal city to describe the metropolarities and the restructured social mosaic of today s urban landscape or postmetropolis . In his book, Postmetropolis Critical Studies of Cities and Regions , he discusses how the contemporary American city has become far more complex than the familiar upperclass vs. middleclass or black vs. white models of society. It has become a fractal city of intensified inequalities and social polarization . The term fractal gives it the idea of having a fractured social geometry. This is a patterning of metropolarities , or an intesification of socio economic inequalities, some of which Soja tries to pinpoint and discuss. Topics The Removal of Distance William Wilson s location theory tries to give an explanation for the widening poverty and inequality gap. With rise of new technologies in recent decades, the new communication methods have allowed us to process and transmit information over great distances. This has, in a sense, destroyed distance. Distance no longer hinders communication as much as it used to. As a result, many businesses have relocated out of the inner city to the suburbs. Sadly, this leaves many ethnic communities stranded in the deindustrialization deindustrialized inner city. They are unable to take part in the sudden shift to information based and service based industry jobs. Both Edward Soja and Saskia Sassen have written on this. Mono Ethnic Geographies Soja uses Los Angeles as evidence that social inequalities and polarizations in American society have in fact been increasing, which partly due to globalization and economic restructuring. He describes the ethnic quilt of L.A., a heterogeneous mosaic of new and old ethnicities . In this, he discusses ethnic niches as well as segregated cityspace, the spatial or geographical concentration of ethic groups in L.A. Many parts of Los Angeles have experienced rapid demographic transformations in recent ... more details
saved book title subtitle cover image cover color Fractal Analysis A Wikipedia Collection compiled by Loren Cobb Fractal dimension Fractal analysis Box counting Multifractal system Entropy information theory R nyi entropy Hausdorff dimension ... more details
Unsourced image removed Image Fractal model.jpg thumb 250px Fractal logo Fractal is a modular and extensible ... system s to middleware platforms and to graphical user interface s. The goal of Fractal is to reduce ... projects in particular. The Fractal model already uses some well known design patterns, such as Unit ... work to get even closer to this goal. Fractal is hosted and developed by the OW2 consortium. It is distributed under the LGPL open source license . Sub Projects The Fractal Project is made of four sub projects The Component Model sub project deals with the definition of the Fractal component model ... in composite components hence the Fractal name and reflexivity components have full introspection and intercession capabilities . The Fractal model is also language independent, and fully modular and extensible. The Implementations sub project deals with the implementation of Fractal component platforms, which allow the creation, configuration and reconfiguration of Fractal components. Julia, the reference ... with the implementation of reusable, ready to use Fractal components, such as protocol or Swing components. The Tools sub project deals with the implementation of Fractal based applications dedicated to Fractal, such as tools to define and manage component configurations . Implementations Besides ... in the ObjectWeb Fractal project, there are several other implementations of the Fractal component ... of mixins. It can execute the same applications as Julia, including Fractal RMI, Fractal ADL, Fractal Explorer. FracTalk is a SmallTalk implementation of the Fractal component model. FractNet http www adele.imag.fr fractnet is a Microsoft .NET Framework .Net implementation of the Fractal component model. Plasma is a C implementation of Fractal, geared at multimedia applications. ProActive http proactive.inria.fr is a distributed and asynchronous implementation of Fractal geared at Grid Computing. ObjectWeb Think Think is a C implementation of Fractal geared at operating system development. Cecilia ... more details
This is a list of fractal topics , by Wikipedia page, See also list of dynamical systems and differential equations topics . 1 f noise Apollonian gasket Attractor Box counting dimension Cantor distribution Cantor dust Cantor function Cantor set Cantor space Chaos theory Coastline Constructal theory Dimension Dimension theory Dragon curve Fatou set Fractal antenna Fractal art Fractal compression Fractal flame Fractal landscape Fractal transform Fractint Graftal Gravity set Iterated function system Horseshoe map How Long Is the Coast of Britain? Statistical Self Similarity and Fractional Dimension Julia set Koch snowflake L system Lebesgue covering dimension L vy C curve L vy flight List of fractals by Hausdorff dimension Lorenz attractor Lyapunov fractal Mandelbrot set Menger sponge Minkowski Bouligand dimension Multifractal analysis Olbers paradox Perlin noise Power law Rectifiable curve Scale free network Self similarity Sierpinski carpet Sierpi ski curve Sierpinski triangle Space filling curve T Square fractal Topological dimension Category Mathematics related lists Fractals Category Fractals ... more details
Image Burning Ship Fractal Overview.jpg thumb High quality overview image of the Burning Ship fractal Image Burning Ship Left.jpg thumb High quality image of the large ship in the left antenna The Burning Ship fractal , first described and created by Michael Michelitsch and Otto E. R ssler in 1992, is generated by iterating the function math z n 1 operatorname Re left z n right i operatorname Im left z n right 2 c, quad z 0 0 math in the complex plane math mathbb C math which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The mapping is non analytic because its real and imaginary parts do not obey the Cauchy&ndash Riemann equations . ref Michael Michelitsch and Otto E. R ssler 1992 . The Burning Ship and Its ... Burning Ship Fractal renderings align center height 125 lines 5 File Burning Ship 3e 9.jpg High quality ... The Burning Ship fractal File Burning Ship Fractal Zoom.png A zoom in to the lower left of the Burning Ship fractal, showing a burning ship and self similarity to the complete fractal. File Burning Ship Fractal Zoom 2.png A zoom in to line on the left of the fractal, showing nested repetition ... Ship fractal. File Jentererforetrukket.jpg The Burning Ship Fractal featured in the 1K intro JenterErForetrukket by Youth Uprising a demoscene production. See also Mandelbrot set Julia set Fractal ... of the Burning Ship fractal , featured by Theory.org, http ozviz.wasp.uwa.edu.au pbourke fractals burnship Burning Ship Fractal , Description generated by a C source code. http www.graphicandfractalworld.com ... Fractal webpage includes the first representations and the original paper cited above on the Burning Ship fractal. http www.fractalforums.com index.php?action gallery sa view id 4057 3D representations of the Burning Ship fractal Category Fractals geometry stub fr Fractale burning ship hr Goru i brod ... more details
Multiple issues wikify February 2012 pov check July 2008 original research April 2008 The fractal approach to soil mechanics is a new line of thought. There are several problems in soil mechanics which can be dealt with by applying a fractal approach. One of these problems is the determination of soil water characteristic curve also called water retention curve and or capillary pressure curve . Its determination is a time consuming process considering usual laboratory experiments. Many scientists have been involved in making mathematical models of soil water characteristic curve SWCC in which constants are related to the fractal dimension of pore size distribution or particle size distribution of the soil. After the great mathematician Beno t Mandelbrot father of fractal mathematics showed the world fractals, scientists of agronomy, agricultural engineering and earth scientists have developed more fractal based models. It is noteworthy that almost all of these models have been used to extract hydraulic properties of soils and the potential capabilities of fractal mathematics to investigate mechanical properties of soils have been overlooked. Therefore, it is really important to use such physically based models to promote our understanding of the mechanics of the soils. That is why it can be of great help for researchers in the area of unsaturated soil mechanics. Not only determination of SWCC but also mechanical parameters can be driven from such models and of course it needs further works and researches. Category Soil mechanics Category Fractals soil sci stub Hydrology stub ... more details
Fractal generating software is any computer program that generates images of fractals . There are many fractal generating programs available, both free and commercial. Features Many different features are included in fractal generating software packages. Most feature some form of algorithm selection, an interactive image zoom, and the ability to save files in JPEG , TIFF or Portable Network Graphics PNG format, as well as the ability to save parameter files, allowing the user to easily return to previously created images for later modification or exploration. Many packages also allow the user to input their own formulae, to allow for greater control of the fractals, as well as a choice of color rendering, along with the use of filters and other image manipulation techniques. Some fractal software packages allow for the creation of movies from a sequence of fractal images. Some standard graphics software such as GIMP contains filters or plug ins which can be used for fractal generation. Many stand alone fractal generating programs can be used in conjunction with other graphics programs such as Photoshop to create more complex images. External links No More Links PLEASE BE CAUTIOUS IN ADDING MORE LINKS TO THIS ARTICLE. WIKIPEDIA IS NOT A COLLECTION OF LINKS NOR SHOULD IT BE USED FOR ADVERTISING. Excessive or inappropriate links WILL BE DELETED. See Wikipedia External links & Wikipedia Spam for details. If there are already plentiful links, please propose additions or replacements on this article s discussion page, or submit your link to the relevant category at the Open Directory Project dmoz.org and link back to that category using the dmoz template. No More Links http www.dmoz.org Science Math Chaos and Fractals Software Science Math Chaos and Fractals Software &ndash list of fractal generating software in Open directory project Open Directory Project References reflist Category Fractals Category Computer art Category Graphics software graphics software stub ru ... more details
In probability and statistics , the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank. This can markedly improve the fit over a simple power law relationship see references below . In a number of applications, there is a so called King effect where the highest ranked item has a significantly greater frequency or size than the model predicts on the basis of the other items. Definition The probability mass function is given, as a function of the rank n , by math f n b,c propto n b exp c log n 2 , math where b and c are paramerers of the distribution. See also Zipf s law References Laherr re J, Deheuvels P 1996 http www.hubbertpeak.com laherrere fractal.htm Distributions de type fractal parabolique dans la nature French, with English summary Parabolic fractal distributions in nature , http www.hubbertpeak.com laherrere fractal.htm Comptes rendus de l Acad mie des sciences , S rie II a Sciences de la Terre et des Plan tes , 322, 7 , 535&ndash 541 cite doi 10.1016 S1674 5264 09 60017 X ProbDistributions discrete infinite DEFAULTSORT Parabolic Fractal Distribution Category Discrete distributions Probability stub fr Distribution fractale parabolique ... more details
Infobox book name The Fractal Geometry of Nature image image caption author Beno t Mandelbrot country United States language English subject Mathematics genre Science publisher W. H. Freeman and Co. release date 1982 media type book pages isbn ISBN 0 7167 1186 9 oclc The Fractal Geometry of Nature is an influential book published in 1982 by the French people Franco USA American mathematics mathematician Beno t Mandelbrot . It is a revised and enlarged version of his 1977 book entitled Fractals Form, Chance and Dimension , which in turn was a revised, enlarged, and translated version of his 1975 French book, Les Objects Fractals Forme, Hasard et Dimension . The books together comprise one of the ten most influential scientific essays of the 20th century American Scientist magazine, 1999 . The impact and persuasiveness of these three books in the scientific community were significantly enhanced using mathematically accurate, computer drawn illustrations created by programmers working with Mandelbrot, primarily at IBM Research. Early drawings were low resolution black and white later drawings were higher resolution and in color, corresponding to the nascent and then quickly evolving computer graphic machinery of the times. See also Fractal Mandelbrot set Chaos theory mathematics lit stub DEFAULTSORT Fractal Geometry of Nature, The Category 1982 books Category Mathematics books ... more details
notability date July 2010 Infobox VG title Fractal developer Cipher Prime engine ActionScript release date s May 2010 genre Video puzzle game Puzzle , Strategy Game Strategy modes Single player ratings NR platforms Personal Computer Fractal is a Video puzzle game puzzle game from Philadelphia, Pennsylvania Philadelphia based studio Cipher Prime . The game involves pushing hexagonal fragments together to form large hexagons and chain reactions. In January 2012 it was offered, along with Nuclear Dawn , Max & the Magic Marker , and Super Crossfire as part of the Pay what you want Indie Royale New Year s Bundle. ref http www.indieroyale.com Indie Royale ref References Reflist puzzle videogame stub Category Puzzle video games ... more details
Unreferenced date September 2009 Infobox album See Wikipedia WikiProject Albums Name Parasite Type Album Artist Fractal Glider Cover Released 2002 Genre Psytrance Length Label Boom Records Producer Paul McCosh Reviews Track listing Skanda s Tail Mezmorized Telementery Karmic Implications Language Of Silence Raspy Honks Colonization Witch Doctor Earth Tremors Personnel Paul McCosh DEFAULTSORT Parasite Album Category 2002 albums Category Psychedelic trance albums ... more details
Infobox radio show show name Seymour the Fractal Cat image imagesize caption other names format Comedy Science fiction runtime 30 minutes country United Kingdom language English language English home station BBC Radio 4 syndicates television starring Paul Bown br John Hegley br Greg Proops br Nisha Nayar br Robert Bathurst creator writer Gary Parker director producer executive producer narrated record location first aired April 1996 last aired num series 1 num episodes 5 audio format Stereophonic sound opentheme I Almost Had a Weakness br by Elvis Costello endtheme website podcast Seymour the Fractal Cat is a science fiction comedy serial featuring Paul Bown , John Hegley and Greg Proops . It was written by Gary Parker , and first broadcast on BBC Radio 4 in 1996. It is rebroadcast from time to time on BBC Radio 7 . Plot summary Computer programmer Jeremy Stone Paul Bown has been let go by his somewhat sinister employer. He makes use of his free time to create his dream program, the Chaos Analysis Transformer , or CAT. He does not know that his computer Omni Tec voiced by John Hegley is part of the Large Artificial Intelligence Network LAIN and is therefore sentient. Omni Tec uses the CAT to re wire the brain of Jeremy s cat Seymour, making him also intelligent and self aware. Seymour is voiced by Greg Proops. There then follows a series of comic misadventures, as Jeremy tries to deal with Seymour s ability to talk. He consults a psychiatrist, Natalie Nisha Nayar who becomes embroiled in the tangled events as Jeremy s former employer attempts to steal the CAT and also use LAIN to further its aim to dominate the world of the Internet. Jeremy turns to his friend Michael Robert ... Attractors Fractal Infinity Simplexity Phase Space Catastrophe Theory External links BBC programme id b009t2jl title Seymour the Fractal Cat http epguides.com SeymourtheFractalCat Entry at epguides.com ... programmes s se seymour the fractal cat.html Entry at radiolistings.co.uk DEFAULTSORT Seymour The Fractal ... more details
the number of boxes needed to cover the network and the size of the box, so called fractal scaling ... for calculation of the dimension Generally we calculate the fractal dimension using either the Box ... of linear size math l B math , needed to cover the given network. The fractal dimension math ... M B left l B right right rangle math for different box sizes, the fractal dimension math d B math .... In order to measure the fractal dimension of networks we add the concept of renormalization. Fractal ... be used as shown above to measure the fractal dimension of the network. In Fig. 3b , renormalization ... center Skeleton and Fractal Scaling The fractal properties of the network can be seen in its underlying ... from the degree of the original network. For the fractal networks following fractal scaling, each skeleton shows fractal scaling similar to that of the original network. The number of boxes ... world fractal networks Image Www.jpg thumb left 200px Fig. 5 Invariance of the degree distribution ... 300px Fig. 6 Fractal scaling analysis of WWW network. Red the original network, Blue the skeleton ... ref Since fractal networks and their skeletons follow the relation center math left langle M B left l B right right rangle sim l B d B math , center we can investigate whether a network is fractal and what is the fractal dimension of the network. For example, the WWW, metabolic network, protein interaction network PIN of H . sapiens , and PIN of S . cerevisiae are considered as fractal networks. Furthermore, the fractal dimensions measured are math d B 4.1, mbox 3.4, mbox 2.0, mbox and 1.8 math ... for instance, the BA model do not show the fractal characteristics fractal properties . ref name kim ... references DEFAULTSORT Fractal Dimension On Networks Category Network theory ... more details
Unreferenced date December 2009 Orphan date December 2009 Infobox Album See Wikipedia WikiProject Albums Name Fractle Notes and Shoe Throats Type Album Artist Positive Infinity Cover Released November 16, 2005 Recorded JD Productions Studio Genre Rock music Rock Length 35 65 Label JD Productions Producer Jonathan Roberts Reviews Last album This album Fractal Notes and Shoe Throats br 2005 Next album How Not to Die in Less Than 24 Hours br 2005 Fractal Notes and Shoe Throats is an emo music emo , Rock music rock album written and performed by Positive Infinity . The album was released on November 16, 2005. Track listing Music written by Jonathan Roberts All lyrics written by Jonathan Roberts Truth The Smoking Gun small 3 04 small Avatar small 2 30 small Being Thorough is Dangerous small 3 26 small Wheel Reinventing Practicality small 4 22 small Leaving Thorns on Roses small 11 51 small Smiles Can t Vivify a Soul small 2 56 small Thus Far and no Further small 0 44 small Broken Reels small 8 32 small Band line up Jonathan Roberts Guitar Bass Lead Vocals Mixing Jah Wobble Percussion Bass Mixing David Ayers Acoustic Guitar Additional credits Produced by Jonathan Roberts Ja Wobble and David Ayers provided material for Avatar and Broken Reels . DEFAULTSORT Fractal Notes And Shoe Throats Category 2005 debut albums Category Positive Infinity albums ... more details
Unreferenced stub auto yes date December 2009 Extreme cinema is a term typically used to describe films containing violence, gore,and sex of an extreme nature. In recent years, the term has been a popular word to describe many of the violent films coming out of Asia particularly Hong Kong , Japan and South Korea . Some of the more notorious extreme filmmakers include Takashi Miike , Park Chan Wook , Shinya Tsukamoto , Sion Sono and Kim Ki Duk . See also J Horror K Horror Splatter film Pink film Tartan Films , United Kingdom based film distributor that have released numerous Extreme cinema titles under their Tartan Asia Extreme label. DEFAULTSORT Extreme Cinema Category Film and video terminology Film term stub ... more details
Fractal Audio Axe Fx is an all in one electric guitar preamplifier effects processor made by Fractal Audio Systems LLC., in Plaistow, New Hampshire . The processor is a two space rack unit . The first version, called simply Axe Fx , was introduced in 2006. Axe Fx Ultra was introduced in 2008. Both of these models were discontinued in June 2011 when a new unit, the Axe Fx II was introduced. The Axe Fx is what is considered a amplifier modeling modeling preamp , simulating the sound of other well known guitar and bass amplifiers, as well as including some original amplifier sounds and designs, as well as speaker cabinets, guitar effect pedals and studio effects. The Axe FX has gained a steadily increasing reputation through online guitar forums such as sevenstring.org and usage by musicians such as John Petrucci , Steve Vai , Devin Townsend and Periphery band Periphery , amongst others. Features The Axe FX is a digital preamplifier and effects processor for electric guitar and other instruments. The unit consolidates a collection of amplifier simulations, guitar speaker cabinet simulations, and effects into a portable hardware format that can be used for music performance, studio recording, or other applications. The unit was originally introduced in 2006 simply as Axe Fx. A model released in 2008 as Axe Fx Ultra contained more DSP processing power and onboard memory. In June 2011, Fractal Audio Systems discontinued both products in favor of the Axe Fx II which bundled additional upgrades and improvements, announcing that the new unit has twice the power of the former flagship, Axe Fx Ultra. The programmable Axe Fx offers flexibility through a large number of adjustable parameters and various routing capabilities. Fractal Audio Systems also created accompanying computer based editing software called Axe Edit and a MIDI foot controller called the MFC 101. The graphical user ... Effects units ru Fractal Audio Systems ... more details
Unreferenced date December 2006 Infobox album See Wikipedia WikiProject Albums Name Extreme The Collection Type Compilation Artist Extreme band Extreme Cover Released 2002 Recorded Genre Heavy metal music Heavy metal , Funk metal Label A&M Records A&M Last album Waiting for the Punchline br 1995 This album Extreme The Collection br 2002 Next album Saudades de Rock br 2008 Extreme The Collection is the second greatest hits album by Extreme band Extreme . After the lack of success of Waiting for the Punchline , the band subsequently disbanded. Track listing Mutha Don t Wanna Go To School Today Little Girls Kid Ego Wind Me Up When I m President More Than Words It s A Monster Decadence Dance Hole Hearted Get The Funk Out Song For Love Cupid s Dead Warheads Hip Today There Is No God nowiki nowiki Misspelt as Mutha Don t Want To Go To School Today . nowiki nowiki Misspelt as Songs For Love . Extreme Category Extreme albums Category 1998 compilation albums Category A&M Records compilation albums 1990s metal album stub pt Extreme The Collection ... more details
Other uses Image Extreme points illustration.png thumb right A convex set in light blue, and its extreme points in red. In mathematics , an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S . Intuitively, an extreme point is a vertex of S . The Krein Milman theorem states that if S is convex and compact space compact in a locally convex space , then S is the closed convex hull of its extreme points In particular, such a set has extreme points. The Krein Milman theorem is stated for locally convex topological vector spaces. The next theorems are stated for Banach space s with the Radon Nikodym property A theorem ... set closed and bounded set has an extreme point. In infinite dimensional spaces, the property of compact ... bang bang and facial spaces, or Look for the extreme points journal SIAM Review volume ... set is the closed convex hull of its extreme points. Edgar s theorem implies Lindenstrauss s theorem. k extreme points More generally, a point in a convex set S is k extreme if it lies in the interior ..., an extreme point is also a 0 extreme point. If S is a polytope, then the k extreme points are exactly ... extreme points are partitioned into k dimensional open faces. The finite dimensional Krein Milman theorem, which is due to Minkowski, can be quickly proved using the concept of k extreme points. If S is closed, bounded, and n dimensional, and if p is a point in S , then p is k extreme for some k n . The theorem asserts that p is a convex combination of extreme points. If k 0, then it s trivially ... . If the endpoints of the segment are q and r , then their extreme rank must be less than that of p , and the theorem follows by induction. See also Choquet theory Extreme points of Earth Notes references References cite web editor Paul E. Black date 2004 12 17 title extreme point url http ... first1 Ephraim J. last2 Borwein first2 Jonathan M. year 1989 article extreme point encyclopedia ... more details
, J. title Novel Modified Pythagorean Tree Fractal Monopole Antennas for UWB Applications publisher ...?id 32367 Wisfaq.nl ref Uses Image Fractal tree Plate b 2 .jpg thumb The Pythagoras tree rendered more like a living tree . It is possible that the Pythagoras tree would make very useful fractal ... www.phidelity.com blog fractal pythagoras tree Pythagoras tree with different geometries as well ... more details
File Extreme40 iSharesCup Kiel2008 09.jpg thumb Extreme 40 Catamarans iShares Cup 2008 in Kiel The Extreme 40 is a class of sailing catamaran created by TornadoSport and designed by Yves Loday . 40 feet long and constructed of carbon fibre . They have a top speed of about 40 knot unit knots 46 mph, 74 km h and can sail at about 35 knots in 20 25 knots of wind. ref http www.extreme40.org extreme40.asp?pid 152 ref The first extreme 40 was launched in 2005. They are sailed in the Extreme Sailing Series, formerly known as the iShares Cup. Extreme 40 s are essentially a scaled up version of the Tornado sailboat Tornado sailboat used in The Olympics . ref http www.isharescup.com en theboat.asp?id 13273 ref Extreme 40 s are 40 feet long, have a 23 foot beam nautical beam , displace 1250 kilogram s of water, have a mast height of 62 feet and a claimed top speed of 40 knots 46 mph, 74 km h . The mainsail is 75 square metres and the jib is 25 square metres. The Gennaker used for downwind sailing is 110 square metres. ref http www.extreme40.org extreme40.asp?pid 153 ref References reflist External links commonscat http www.extreme40.org YouTube id 63hoN8S4nxY title Extreme 40 boat tour Category Catamarans de Extreme 40 fr Extreme 40 ... more details
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