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Topic: Fractal

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In the News (Thu 23 May 19)

  Fractal Geometry - Crystalinks
The term "fractal" was coined by Benoit Mandelbrot about 1975 to describe a complex geometrical object that has a high degree of "self-similarity" and a fractional dimension that exceeds the normal, or "topological", dimension ("D") for that type of object.
Fractals are said to possess infinite detail, and they may actually have a self-similar structure that occurs at different levels of magnification.
Fractal geometry is the branch of mathematics which studies the properties and behavior of fractals.
www.crystalinks.com /fractal.html   (2219 words)

 Fractal - Wikipedia, the free encyclopedia
Fractals defined by recurrence relations are usually quasi-self-similar but not exactly self-similar.
It should be noted that not all self-similar objects are fractals — e.g., the real line (a straight Euclidean line) is exactly self-similar, but since its Hausdorff dimension and topological dimension are both equal to one, it is not a fractal.
Trees and ferns are fractal in nature and can be modeled on a computer using a recursive algorithm.
en.wikipedia.org /wiki/Fractal   (1859 words)

 Sprott's Fractal Gallery
fractal is automatically generated by a variation of the program included with the book Strange Attractors: Creating Patterns in Chaos by Julien C. Sprott.
The following fractals are iterated function systems generated by the random iteration algorithm using two linear affine transformations.
These images illustrate the stretching that causes chaos and the folding that produces the fractal microstructure of strange attractors.
sprott.physics.wisc.edu /fractals.htm   (1311 words)

 Fractal Geometry
But Mandelbrot conceived and developed a new fractal geometry of nature based on the fourth dimension and Complex numbers which is capable of describing mathematically the most amorphous and chaotic forms of the real world.
Mandelbrot discovered that the fourth dimension of fractal forms includes an infinite set of fractional dimensions which lie between the zero and first dimension, the first and second dimension and the second and third dimension.
For a fractal as a geometric figure not only has irregular shapes - the zig zag world of nature - but there is lurking in the disorder a hidden order in these irregular shapes.
www.fractalwisdom.com /FractalWisdom/fractal.html   (2550 words)

 Fractal Architecture by Michael Ostwald for the Nexus Network Journal vol.3 no.1 Winter 2001   (Site not responding. Last check: 2007-10-21)
The feedback mechanisms and fractal forms associated with order in seemingly chaotic systems are, for Eisenman, a means of destroying the stability of architecture and undermining the anthropomorphic orthodoxy that has sustained architectural theory since Vitruvius.
Fractal geometry, the source of the outbreak, is not necessarily critical to the design; rather it is merely the most "available" of a number of possible sources of "infection".
But the fact remains that his call for a fractal architecture of complexity was not only savaged by the critics, it appears to have been largely ignored by an architectural profession that now considered fractal geometry dated.
www.nexusjournal.com /Ostwald-Fractal.html   (5709 words)

The first relates to 'fractal scaling.' The visual consequence of obeying the same statistics at different magnifications is that it becomes difficult to judge the magnification and hence the length scale of the pattern being viewed.
Furthermore, a survey of fractals measured in physical systems indicates that the average range over which fractals are observed is approximately one order of magnitude [13].
This increase in both canvas size and density of trajectories was accompanied by a rise in the pattern's fractal dimension from 1 to 1.72.
www.phys.unsw.edu.au /PHYSICS_!/FRACTAL_EXPRESSIONISM/fractal_taylor.html   (2193 words)

 FRACTAL CHAOS: the Philosophy of Freedom and Self Determination
It is possible to apply this new knowledge to better understand your life, to live autonomously, based on freedom, and your own contact with the Source of the Universe, the Infinite.
These fractals are in space, as shown by the graphics on these webs, and in time, as shown in all life, including your own.
This is a new kind of order, a "fractal order," based on a relatively few basic structural principals from which many transitory laws follow.
www.schoolofwisdom.com /FractalWisdom   (2073 words)

 sci.fractals FAQ   (Site not responding. Last check: 2007-10-21)
Fractals also describe many real-world objects, such as clouds, mountains, turbulence, coastlines, roots, branches of trees, blood vesels, and lungs of animals, that do not correspond to simple geometric shapes.
Roughly, fractal dimension can be calculated by taking the limit of the quotient of the log change in object size and the log change in measurement scale, as the measurement scale approaches zero.
Topics include: challenges of using fractals in the classroom, new ways of generating art and music, the use of fractals in clothing fashions of the future, fractal holograms, fractals in medicine, fractals in boardrooms of the future, fractals in chess.
www.faqs.org /faqs/sci/fractals-faq   (12472 words)

 Sekino's Fractal Gallery
Nature is filled with fractals as seen in such objects as mountains, shorelines, trees (branches, barks and roots), ferns, fluid flow patterns, cloud formations (with or without lightning), blood vessels and mycelial strands, whence fractals, we believe, project mathematical light on natural phenomena that are beyond the reach of Euclidean geometry.
If we type "fractal gallery" in the Internet search engine Google, we will immediately receive a list of tens of thousands of web sites that display a variety of computer-generated fractal images, many of which are strikingly beautiful.
Each of the fractals we consider here is generated by a single equation and they may be classified into three categories, Mandelbrot, Julia, and Newton patterns, to be discussed one at a time.
www.willamette.edu /~sekino/fractal/fractal.htm   (2548 words)

Examples of self similarity in fractals with examples from mathematics and photos of the physical world.
The real world was full of larger structures, smaller structures, simpler and more complex structures than the tiny portion comprising sentient creatures and their societies, and it required a profound myopia of scale and similarity to believe that everything beyond this shallow layer could be ignored.
Fractal terrain modelling manual and an application for the Macintosh.
astronomy.swin.edu.au /~pbourke/fractals   (457 words)

 Fractal Antenna Systems Inc: The World's Smallest Wideband and Multiband Antennas
Fractal antennas have superior multiband performance and are typically two-to-four times smaller than traditional aerials.
Fractal Antenna Systems, Inc., designs and manufactures the most compact and powerful antennas in the world.
Used in the most demanding commercial, military and government applications, Fractal Antenna’s products deliver unprecedented frequency coverage, versatility, and performance in form factors that are a fraction of the size of traditional antennas.
www.fractenna.com   (137 words)

Fractals are any pattern that reveals greater complexity as it is enlarged A real-life example of fractals is ice crystals freezing on a glass window.
Fractals appear to be complex and hard-to-comprehend at first glance, but the underlying code is very simple.
This fractal gallery is divided into five parts (use either text or images to navigate to them) containing over 25 images.
www.42explore.com /fractal.htm   (877 words)

 Welcome to the Fractal eXtreme Web Site
Improved fractal plugins for Fractal eXtreme are released, for faster exploration of the Mandelbrot set and other fractals.
Fractal eXtreme Zoom Movie Plug-in 1.11 is released, allowing the playing of unique animated zooms into fractals on web pages.
The ideal fractal exploration program should give you enough features to let you do whatever you want, and should be fast enough to handle the computational complexity of fractal calculations.
www.cygnus-software.com   (422 words)

 Fractal Software Links on Paul N. Lee's website
Additional information may also be found within the Fractal Census, where over 4,000 individuals are listed (plus statistics on software use and number of users per country).
This program graphs fractals based on 3X3 matrices, where a Latin square is combined with a sign matrix and the composite matrix is iterated the same as a complex or quad variable.
Fractal Agent is the intro version, Fractal Commander the 256-color version, and Fractal Elite the true-color version.
home.att.net /~Paul.N.Lee/Fractal_Software.html   (3167 words)

 Fractal - Home Page
Fractal is a modular and extensible component model that can be used with various programming languages to design, implement, deploy and reconfigure various systems and applications, from operating systems to middleware platforms and to graphical user interfaces.
Plasma is a C++ implementation of Fractal, geared at multimedia applications.
Think is a C implementation of Fractal geared at operating system development.
fractal.objectweb.org   (353 words)

 Fractal Art
Fractal art is the visual depiction of complex mathematical equations.
Fractal geometry is to a digital artist as a brush is to a painter: a tool for the expression of visual ideas.
It's a world in which fractal geometry dictates reality, from geography to biology, just as the laws of physics dictate the reality of your familiar everyday world.
www.fractalism.com /fractal-art.htm   (159 words)

 Fractal Frequently Asked Questions and Answers
Roughly, fractal dimension can be calculated by taking the limit of the quo- tient of the log change in object size and the log change in measurement scale, as the measurement scale approaches zero.
The aim of this first international journal on fractals is to bring together the most recent developments in the research of fractals so that a fruitful interaction of the various approaches and scientific views on the complex spatial and temporal behavior could take place.
NOTICE from Noel Giffin (noel@erich.triumf.ca): Welcome to the Spanky Fractal Database This is a collection of fractal's and fractal related material for free distribution on the net.
www.faqs.org /faqs/fractal-faq   (9659 words)

 Welcome to the Fractal Foundation
The Fractal Foundation and the LodeStar Astronomy Center announce the beginning of a monthly Fulldome Fractal Show, starting June 2nd.
Invite the Fractal Foundation to bring a fractal presentation to your school.
The Fractal Foundation is a tax-exempt 501c(3) organization.
www.fractalfoundation.org   (174 words)

 Anne's Fractal Menagerie
Most of the fractals on this website were created with Frederik Slijkerman's Ultra Fractal software.
I first became interested in fractals when I happened upon a television program on my local PBS station about them.
I can't tell you how happy and excited I was when I began finding websites about fractals on the Internet and learned that there were software programs like Ultra Fractal with which you could create them yourself.
fractal.sphosting.com   (191 words)

 Download Page
This site is dedicated to Fractal Forge, one of the fastest fractal generating applications available for Windows 95/98/NT/2000/XP.
Fractal Forge is open source and is distributeds under the GNU General Public License.
Fractal Forge is copyright © 1996-2002 by Uberto Barbini.
www.fractovia.org /uberto   (179 words)

 Fractal World Gallery Thumbnails : cosmic recursive fractal flames or flame fractals
pure flame fractals, fractal flame composites, fractals, etc: established 1998
Fractal images from this gallery may only be used with artists permission
Fractal software includes Frax Flame and Apophysis for cosmic recursive fractal flames.
www.enchgallery.com /fractals/fracthumbs.htm   (62 words)

Fractal Edge solutions let you interact with data more effectively and efficiently than ever before.
So whether you're monitoring performance, analyzing risk, managing complex processes, or digesting large reports Fractal Edge technology can help you achieve your goals more efficiently and effectively.
Learn more about how our blue-chip customers are driving greater value from their data.
www.fractaledge.com   (137 words)

 Ultra Fractal: Advanced Fractal Animation Software
Ultra Fractal is the best tool to create fractal artwork and fractal animations.
Whether you are a graphics designer, a professional fractal artist, a video producer, or a complete beginner, Ultra Fractal 4 makes it easy to create beautiful fractal pictures, animated textures, and moving fractal backgrounds.
Enjoy the great Ultra Fractal user community, share your fractals, and get help on the Ultra Fractal mailing list.
www.ultrafractal.com   (179 words)

 Exploring Fractals   (Site not responding. Last check: 2007-10-21)
It is is based on a curriculum, entitled "Exploring Fractal Dimension," developed by
Its revision entitled "Exploring Fractals: From Cantor Dust to The Fractal Skewed Web" has been edited by Mary Ann Connors 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, and 2004.
"Fractals", a modified version of Exploring Fractals, is a Case Study in the Calculus/Math Modules published by PWS Kent.
www.math.umass.edu /~mconnors/fractal/fractal.html   (199 words)

 Cynthia Lanius' Fractals Unit: Fractal Dimension
A fractal might have dimension of 1.6 or 2.4.
Remember as we continue that fractals are really formed by infinitely many steps.
Note 3: Robert Devaney has more information on fractal dimension.
math.rice.edu /~lanius/fractals/dim.html   (596 words)

 Waterloo Fractal Coding Page   (Site not responding. Last check: 2007-10-21)
The Waterloo Fractal Compression Project is part of a general research programme dedicated to the study of fractal analysis and Iterated Function Systems/Fractal Transforms from both theoretical as well as practical perspectives.
It is also part of a international collaborative project involving the University of Waterloo, Ecole Polytechnique de l'Universite de Montreal, the University of Verona and INRIA Rocquencourt, France.
One of the primary goals of this collaboration is to develop a new generation of image and signal compression methods which incorporate "fractal based" methods.
links.uwaterloo.ca   (371 words)

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