Analysis on fractals or calculus on fractals is a generalization of Differentiable manifold calculus on smooth manifolds to calculus on fractals . The theory describes dynamical phenomena which occur on objects modelled by fractals. It studies questions such as how does heat diffuse in a fractal? and How does a fractal vibrate? In the smooth case the operator that occurs most often in the equations modelling these questions is the Laplacian , so the starting point for the theory of analysis on fractals is to define a Laplacian on fractals. This turns out not to be a full differential operator in the usual sense but has many of the desired properties. There are a number of approaches to defining the Laplacian probabilistic, analytical or measure theoretic. See also Time scale calculus for dynamic equations on a cantor set . Differential geometry Discrete differential geometry Abstract differential geometry References cite book author Christoph Bandt, Siegfried Graf, Martina Z hle title Fractal Geometry and Stochastics II publisher Birkh user year 2000 isbn 9783764362157 cite book author Jun Kigami title Analysis on Fractals publisher Cambridge University Press year 2001 isbn 9780521793216 cite book author Robert S. Strichartz title Differential Equations on Fractals publisher Princeton year 2006 isbn 9780691125428 cite book authors Pavel Exner, Jonathan P. Keating, Peter Kuchment, Toshikazu Sunada, and Alexander Teplyaev title Analysis on graphs and its applications Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 8 June 29, 2007 publisher AMS Bookstore year 2008 isbn 9780821844717 External links http www.ams.org notices 199910 fea strichartz.pdf Analysis on Fractals , Robert S. Strichartz Article in Notices of the AMS http www.math.uconn.edu teplyaev fractals University of Connecticut Analysis on fractals Research projects http adsabs.harvard.edu abs 2003math.ph..10047P, Calculus on fractal subsets of real line I formulation Category Fractals ... more details
italictitle Infobox Journal title Fractals cover discipline Fractal s publisher World Scientific country Singapore website http www.worldscinet.com fractals fractals.shtml ISSN 0218 348X eISSN 1793 6543 Fractals is a Peer review peer reviewed scientific journal devoted to explaining complex phenomena using fractal geometry and scaling. It is an inter disciplinary journal published by World Scientific and has explored diverse topics from turbulence and colloid al aggregation to stock market s. Abstracting and indexing The journal is abstracted in Science Citation Index ISI Alerting Services Current Contents Physical, Chemical & Earth Sciences Mathematical Reviews Inspec CSA Calcium and Calcified Tissues Abstracts CSA Pollution Abstracts CSA Aquatic Sciences and Fisheries Abstracts ASFA CSA Selected Water Resources Abstracts CSA Microbiology Abstracts Zentralblatt MATH Compendex Category Mathematics journals Category English language journals Category World Scientific academic journals ... more details
Genuine Fractals ref http www.pcpro.co.uk macuser reviews 15870 genuine fractals.html?searchString fractal MacUser product review ref ref http www.imaging resource.com SOFT GF GF.HTM Imaging Resources product review ref ref http www.graphics.com modules.php?name News&file article&sid 3590 graphics.com product review ref ref http www.macnn.com articles 07 01 25 genuine.fractals.5.beta Mac News article ref ref http www.designpreference.com reviews software genuinefractals5.html DesignPreference product review ref is a Adobe Photoshop Photoshop plug in developed and distributed by onOne Software of Portland, Oregon . The original Windows version of Genuine Fractals was designed and developed by Altamira Group in Burbank, California under team leader Steven bender Steven Bender in 1996. In 1997, Altamira released the Robert McNally developed Version 2.0 on the Macintosh Platform and the redesigned the Windows Version 2.0 product. The Genuine Fractals products were acquired by MrSID LizardTech in June 2001, before ultimately being acquired by onOne Software in July 2005. The current version, 7.0, was renamed Perfect Resize 7.0 by onOne software. There are two main features in the Genuine Fractals plug in. First is a feature to save image files in either FIF Fractal Image Format or its ... 1 for lossless and 5 1 for visually lossless. The second main feature of Genuine Fractals is a scaling ... . When scaling up, Genuine Fractals exploits the self similarity of an image to increase its size while preserving detail. In 1997, Genuine Fractals won a MacWorld Eddy. ref http prwire.com cgi bin stories.pl?ACCT 104&STORY www story 1 7 98 389101&EDATE MacWorld 1997 EDDY winners, Genuine Fractals wins Best Graphics Plug in ref Notable also because Genuine Fractals was the first product developed ... software computers 0306genuine index.html , Genuine Fractals 4.1 Resampling With GF Might Make ... www.ononesoftware.com detail.php?prodLine id 2 Genuine Fractals http www.google.com patents?id Hv1 ... more details
Infobox Book name The Beauty of Fractals title orig translator image Image BeautyOfFractalsBook.jpg 150px image caption Cover author Heinz Otto Peitgen , Peter Richter illustrator cover artist country language series subject Fractals genre publisher Springer Verlag, Heidelberg release date 1986 english release date media type pages isbn 0 387 15851 0 dewey 516 19 congress QA447 .P45 1986 oclc 13331323 preceded by followed by The Science of Fractal Images The Beauty of Fractals is a 1986 book by Heinz Otto Peitgen and Peter Richter which publicises the fields of Dynamical system complex dynamics , chaos theory and the concept of fractal s. It is lavishly illustrated and as a mathematics book became an unusual success. The book includes a total of 184 illustrations, including 88 full colour pictures of Julia sets. Although the format suggests a coffee table book , the discussion of the background of the presented images addresses some sophisticated mathematics which would not be found in popular science books. In 1987 the book won an Award for distinguished technical communication. Summary The books starts with a general introduction to Dynamical system Complex Dynamics , Chaos theory Chaos and Fractals . In particular the Mitchell Feigenbaum Feigenbaum scenario and the relation to Julia Sets and the Mandelbrot set is discussed. The following special sections provide in depth detail for the shown images Verhulst Dynamics, Julia Sets and Their Computergraphical Generation, Sullivan ... Mandelbrot gives a very personal account of his discovery of fractals in general and the fractal named ... Cardinal location London isbn pages 229 ref ref Fractals The Patterns of Chaos. John Briggs. 1992 ... of the Mandelbrot set s structure is to beg, borrow, steal or I recommend buy The Beauty of Fractals ... pages 100&ndash 124 ref The Beauty of Fractals provided the first such publication within a book. border ... DEFAULTSORT Beauty Of Fractals, The Category 1986 books Category Science books Category Mathematics ... more details
1990 & 2003 isbn 0 470 84862 6 nopp true page xxv ref Presented here is a list of fractals ordered ... a low or a high dimension. Deterministic fractals border 0 cellpadding 4 rules all style border ... math 0 D 1 math . ref http arxiv.org abs 0911.2497 The scattering from generalized Cantor fractals ... and Fractals isbn 0 387 98993 5 ref . Calculated align right 1.0812 Julia set z 1 4 align center Image ... tangent circles in red . Also an Apollonian packing. See ref http classes.yale.edu Fractals CircInvFrac ... 150px cf. Chang & Zhang. ref http poignance.coiraweb.com math Fractals Dragon Bound.html Fractal dimension ... product.png 150px Generalization Let FxG be the cartesian product of two fractals sets F and G ... be extended in 3D. ref http www.mathcurve.com fractals lebesgue lebesgue.shtml Lebesgue curve ... trose rossler.html Fractals and the R ssler attractor ref Measured align right 2.06 ... metallic fractals and their photonic crystal characteristics publisher Phys. Rev. B 77 , 125113 ... fractals border 0 cellpadding 4 rules all style border 1px solid 999 background color FFFFFF align ... of Norway align center Image Norway municipalities.png 100px See J. Feder. ref Feder, J., Fractals, , Plenum ... fractals FracAndDim BoxDim PowerLaw CrumpledPaper.html title Power Law Relations first last date ... Meakin 1987 ref See also Commons Fractal fractals Fractal dimension Hausdorff dimension Scale invariance ..., Fractals Everywhere , Morgan Kaufmann ISBN 0 12 079061 0 Bernard Sapoval, Universalit s et fractales ... search ?query fractal The fractals on Mathworld http local.wasp.uwa.edu.au pbourke fractals Other fractals on Paul Bourke s website http soler7.com Fractals FractalsSite.html Soler s Gallery http www.mathcurve.com fractals fractals.shtml Fractals on mathcurve.com http 1000fractales.free.fr index.htm 1000fractales.free.fr Project gathering fractals created with various softwares http library.thinkquest.org 26242 full index.html Fractals unleashed Use dmy dates date September 2010 DEFAULTSORT List ... more details
Notability date August 2010 Hartmut J rgens is a Germany German mathematician , born in 1955 in Bremen city Bremen, Germany . ref Fractals for the classroom strategic activities, Vol. 2, Spinger Verlag 1992, p. vi ref He received his doctorate in 1983 from the University of Bremen . He has worked in the computer industry, and was the Director of the Dynamical Systems Graphics Laboratory at the University of Bremen . He is the co author of both Fractals An Animated Discussion a video and Chaos and Fractals New Frontiers of Science Springer Verlag, ISBN 0387979034 References Reflist Persondata Metadata see Wikipedia Persondata . NAME Jurgens, Hartmut ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1955 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Jurgens, Hartmut Category 1955 births Category Living people Category German mathematicians Category 20th century mathematicians Category 21st century mathematicians Germany mathematician stub ht Hartmut J rgens ... more details
Image Flocon hexagonal.gif 200px left Image hexaflake.gif thumb right The first six iterations of the hexaflake. Image Cantor cube as hexaflake.gif thumb right Orthogonal projection of a cantor cube showing a hexaflake. A hexaflake is a fractal constructed by Iteration iteratively exchanging each hexagon by a flake of seven hexagons it is a special case of the n flake . As such, a hexaflake would have 7 sup n 1 sup hexagons in its n th iteration. Its Boundary topology boundary is the Koch snowflake von Koch flake , and contains an infinite number of Koch snowflakes black or white . Its Hausdorff dimension is equal to ln 7 ln 3 , approximately 1.7712. It is also the projection of the cantor set cantor cube onto the plane orthogonal to its main diagonal. See also List of fractals by Hausdorff dimension External links http www.walkingrandomly.com ?p 626 Quadraflakes, Pentaflakes, Hexaflakes and more includes Mathematica code to generate these fractals Category Fractals geometry stub ... more details
bin stories.pl?ACCT 104&STORY www story 1 7 98 389101&EDATE MacWorld 1997 EDDY winners, Genuine Fractals wins Best Graphics Plug in. Notable also because Genuine Fractals was the first product developed ... GF.HTM Description of Genuine Fractals features and importance http www.ononesoftware.com detail.php?prodLine id 2 Genuine Fractals version 5 from onOne Software http www.adobe.com products plugins photoshop genfrac.html Genuine Fractals from Adobe.com Persondata Metadata see Wikipedia Persondata . NAME ... more details
Image Koch curve.svg thumb The Koch curve, an example of a teragon. Not to be confused with Tarragon . A teragon is a self similar fractal curve that can be produced by replacing each line segment in an initial figure with multiple connected segments, then replacing each of those segments with the same pattern of segments which was used to replace the first figure, and repeating the process an infinite number of times for every line segment in the figure. Teragons are composed of infinitely many segments. Examples of such fractals include the Koch curve and the Peano curve . References Mandelbrot, B.B. 1982 . The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0 7167 1186 9. geometry stub Category Fractals de Monsterkurve ... more details
SpangFract is a fractal generating program for Mac OS Mac OS . SpangFract is one of the few deep fractal generators available for the Macintosh platform. The program currently comes with more than 100 available formulas. It is capable of escape, orbit trap, and dust fractals. It features the ability to create or combine other formulas and coloring methods. Colors may be taken from photos or movies. The current version Spangfract xTel intel Macs only which is compatible on Mac OS X 10.3 and higher including Mac Os X 10.5. Older versions are available that are compatible back to Mac OS 8 See also Fractal generating software External links http groups.yahoo.com group Spangfract Official SpangFract Yahoo Group Category Fractals ... 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
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
The Sierpi ski arrowhead curve is a fractal curve similar in appearance and identical in limit to the Sierpi ski triangle . Image Arrowhead curve 1 through 6.png thumb right 400px Evolution of Sierpi ski arrowhead curve Representation as Lindenmayer system The Sierpi ski arrowhead curve can be expressed by a rewriting rewrite system L system . Alphabet X, Y Constants F, , &minus Axiom XF Production rules X &rarr YF XF Y Y &rarr XF &minus YF &minus X Here, F means draw forward , means turn left 60 , and &minus means turn right 60 see turtle graphics . Like many two dimensional fractal curves, the Sierpi ski arrowhead curve can be extended to three dimensions Image Sierpinski arrowhead 3d stage 5.png 250px Literature Peitgen et al., em Chaos and Fractals em , Springer Verlag, 1992. Roger T. Stevens, em Fractal Programming in C em , M&T Books, 1989. See also List of fractals by Hausdorff dimension Sierpi ski curve DEFAULTSORT Sierpinski arrowhead curve Category Fractals Category Fractal curves ... more details
orphan date January 2010 Dielectric breakdown model DBM is a macroscopic mathematical model combining the diffusion limited aggregation model with electric field . It was developed by Niemeyer, Pietronero, and Weismann in 1984. It describes the patterns of dielectric breakdown of solids, liquids, and even gases, explaining the formation of the branching, self similar Lichtenberg figure s. External links http classes.yale.edu fractals Panorama Physics DLA DBM DBM.html Dielectric Breakdown Model Category Electricity phys stub ... more details
In mathematics , self affinity refers to a fractal whose pieces are scaled by different amounts in the x and y directions. We refer to these as being the 2 dimensional axes, like that of a grid. This means that in order to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic transformation. From http www.dictionary.com www.dictionary.com In physics and botany, the word anisotropy means of unequal physical properties along different axes . geometry stub Category Fractals fr Self affinit zh ... more details
Image Apollonian spheres.jpg thumb right Apollonian sphere packing Apollonian sphere packing is the three dimensional equivalent of the Apollonian gasket . The principle of construction is very similar with any four spheres that are cotangent to each other, it is then possible to construct two more spheres that are cotangent to four of them. The fractal dimension is 2.473946. ref Citation first M. last Borkovec first2 W. last2 De Paris first3 R. last3 Peikert author link publication date date year 1994 title The Fractal Dimension of the Apollonian Sphere Packing periodical Fractals series publication place place publisher volume 2 issue 4 pages 521 526 url http graphics.ethz.ch peikert papers apollonian.pdf issn doi 10.1142 S0218348X94000739 oclc accessdate 2008 09 15 ref Software for generating and visualization of the apollonian sphere packing ApolFrac. ref http thomasbonner.heliohost.org apolfrac.htm ApolFrac ref References references Category Hyperbolic geometry Category Fractals geometry stub it Impacchettamento di sfere apolloniano ... more details
Beno t title Fractals and Chaos publisher Springer location Berlin year 2004 isbn 9780387201580 quote ... 0R2LkE3N7 oC accessdate 1 February 2012 year 1983 publisher Macmillan isbn 978 0 7167 1186 5 ref Fractals ... far ref name Gouyet Fractals may be exactly the same at every scale, or as illustrated in Mandelbrot ... ref As mathematical equations, fractals are usually nowhere differentiable , which means that they cannot ... history roots of the idea of fractals have been traced through a formal path of published works ... century with a subsequent burgeoning of interest in fractals and computer based modelling ... defined. The general consensus is that theoretical fractals are infinitely self similar, iteration iterated , and detailed mathematical constructs having fractal dimensions, of which many List of fractals ... ref name Falconer ref name patterns Cite book title Fractals The Patterns of Chaos last ... isbn 0500276935, 0500276935 page 148 ref Fractals are not limited to geometric patterns, but can also ... ref name music cite doi 10.1142 S0218348X0700337X ref and found in fractals in nature nature , ref name heart ref name heartrate ref name cerebellum ref name neuroscience ref name branching fractals ... and fractals in art art . ref name novel ref name African art ref name fractal painting Introduction ... to uncover finer, previously invisible, new structure. If this is done on fractals, however, no new detail appears nothing changes and the same pattern repeats over and over, or for some fractals, nearly ... for fractals is that the pattern reproduced must be detailed . ref name Mandelbrot1983 ... feature, that fractals as mathematical equations are nowhere differentiable . In a concrete sense, this means fractals cannot be measured in traditional ways. ref name Mandelbrot1983 ref name vicsek ... to the curve. This is perhaps counter intuitive, but it is how fractals behave. ref name Mandelbrot1983 ... of every line segment with a pair of line segments that form an equilateral bump The history of fractals ... 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
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
In mathematics , the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric , to a given set. The IFS described is composed of contraction mapping contractions whose images, as a collage or Union set theory union when mapping the given set, are arbitrarily close to the given set. It is typically used in fractal compression . Statement of the theorem Let math mathbb X math be a complete metric space . Let math L in H mathbb X math be given, and let math epsilon geq 0 math be given. Choose an iterated function system IFS math mathbb X w 1, w 2, dots, w N math with contractivity factor math 0 leq s 1 math , so that math h left L, bigcup n 1 N w n L right leq varepsilon, math where math h d math is the Hausdorff metric. Then math h L,A leq frac varepsilon 1 s math where A is the attractor of the IFS. See also Michael Barnsley References cite book author Barnsley, Michael. title Fractals Everywhere year 1988 publisher Academic Press, Inc. isbn 0 12 079062 9 External links http www.cut the knot.org ctk ifs.shtml A description of the collage theorem and interactive Java applet at cut the knot . http www.math.okstate.edu mathdept dynamics lecnotes node47.html Notes on designing IFSs to approximate real images. Dead link date August 2010 http scimath.unl.edu MIM files MATExamFiles Snyder MAT Exam ExpositoryPaper.pdf Expository Paper on Fractals and Collage theorem DEFAULTSORT Collage Theorem Category Fractals Category Theorems in geometry geometry stub fr Th or me du collage ... more details
Wikify date December 2010 Image Mandelboxpwr2.png alt A three dimensional Mandelbox fractal of scale 2. thumb right A scale 2 Mandelbox Image Mandelboxpwr3.png alt A three dimensional Mandelbox fractal of scale 3. thumb right A scale 3 Mandelbox In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. However, unlike the Mandelbrot set, the mandelbox is defined as a map of continuous Julia set Julia sets , and thus can be defined in any number of dimensions. ref https sites.google.com site mandelbox what is a mandelbox ref As a result, it is an example of a multifractal system . It is typically drawn in three dimensions for illustrative purposes. Generation The iteration applies to vector z as follows function iterate z for each component in z if component 1 component 2 component else if component 1 component 2 component if magnitude of z 0.5 z z 4 else if magnitude of z 1 z z magnitude of z 2 z scale z c Here, c is the constant being tested, and scale is a real number. A notable property of the mandelbox, particularly for scale 1.5, is that it contains approximations of many well known fractals within it. ref http sites.google.com site mandelbox negative mandelbox negative mandelbox ref ref http sites.google.com site mandelbox more negatives more negatives ref ref http www.miqel.com fractals math patterns mandelbox 3d fractal.html mandelbox 3d fractal ref See also Mandelbulb Notes Reflist References citation first Jos last Leys title Mandelbox. Images des Math matiques publisher CNRS year 2010 url http images.math.cnrs.fr Mandelbox.html External links http images.math.cnrs.fr Mandelbox.html Images of some Mandelbox cubes Category Fractals fr Mandelbox ... more details
for generating Lyapunov fractals An algorithm , for computing the fractal is summarized as follows ... in the image plane. External links http www.efg2.com Lab FractalsAndChaos Lyapunov.htm EFG s Fractals ... Hypertextbook url http hypertextbook.com chaos 44.shtml Category Fractals de Ljapunow Diagramm fr ... more details
, a computer program for rendering fractals very quickly on the Intel 80386 processor using ... software Sterling program Sterling References Michael Frame, Beno t B. Mandelbrot , Fractals, Graphics ... Fractals Category Numerical software Category Cellular automaton software Category Graphics software ... more details
Orphan date February 2009 Blobotics is a term describing research into chemical based computer processors based on ions rather than electrons . Andrew Adamatzky , a computer scientist at the University of the West of England in Bristol used the term in an article in New Scientist March 28, 2005 http www.newscientist.com channel fundamentals mg18524921.000 introducing the glooper computer.html . The aim is to create liquid logic gates which would be infinitely reconfigurable and self healing . The process relies on the Belousov Zhabotinsky reaction , a repeating cycle of three separate sets of reactions. Such a processor could form the basis of a robot which, using artificial sensors, interact with its surroundings in a way which mimics living creatures. The coining of the term was featured by Australian Broadcasting Corporation ABC radio in Australia http www.abc.net.au newsradio txt s1363466.htm . References Motoike I., Andrew Adamatzky Adamatzky A. Three valued logic gates in reaction diffusion excitable media. Chaos, Solitons & Fractals 24 2005 107 114 Adamatzky, A. Collision based computing in Belousov Zhabotinsky medium. Chaos, Solitons & Fractals 21 5 , 2004 , p1259 1264 DOI 10.1016 j.chaos.2003.12.068 Category Robotics Robo stub ... 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
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