41. A P R E S S . C O M in your favorite language using a standard graphics library for Linux or Windows that can speedily produce a series of mandelbrot fractals (Z=Z2+C). http://www.apress.com/promo/fractal/

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42. Home -- Hping Packet Generator mandelbrot fractals RealTime Generator 233Gradi, Italian Books Search Engine mandelbrot fractals Generator mandelbrot fractals Real http://wiki.hping.org/

h p i ng wiki HOME RECENT CHANGES CONTACTS DOWNLOAD ... Home Welcome to the hping wiki (see: what's hping ). The aim of this site is to create a collaborative environment to document hping, share programming tips and hping scripts, and much more. Many topics can be discussed here Salvatore Sanfilippo (aka antirez If you want to download source code or binary distributions of hping, go to the Download page. Please, if you think this site is insecure because every page is editable read this Why I can edit every page of this site Most of the vandalized pages here are from people that think they found a vulnerability in the site because all is editable! News Federico Biancuzzi interviewed me about for onlamp.com. The interview can be found here alpha 2 released Download It. hping2.0.0 Release Candidate 3 released. Download It. Starting points of interest What's hping hping3 API Getting started with hping3 Open bugs ... The Tcl Language (See also the local Tcl page). Tclwise - an online book on Tcl authored by the hping author. About this site What's a Wiki How to create a new page (and How to add an image in a wiki page Graffiti (test page, to experiment with this wiki)

43. Spanky Whats-new A page for listing information on the topic of Whats New in Fractals. has a thumbnail thumbnail gallery of mandelbrot fractals created with FractInt. http://spanky.triumf.ca/www/whats-new.html

THE SPANKY FRACTAL DATABASE An interesting mandelbrot. What's New with Spanky It can get confusing browsing these fractal pages in their semi-organized state brought on by my random updating. All the links can be a little overwhelming so I'm going to make an attempt to filter all the new links through this page before moving them to their appropriate index page. If you're just looking for recent developments in the Fractal Community, then this is the page for you. I'll form a small set of links under each of the main information catagories I maintain and just keep pointers to recent additions here. I'll try and keep the number of links low and reasonably up-to-date. This page will have a very simple format, within each catagory, new things will be added to the bottom of the list, and moved to the related index page when they get to the top. This is also one page where the header image may change from time to time. I'll use this page to introduce any current favourite or recent image that I've created. New Fractal Images Other Images directory Les St Clair's les_stclair@compuserve.com

44. Marko Mäkelä's Software Projects: 3D Mandelbrot And Julia Fractals This creates distorted mandelbrot fractals. Please do not expect the program to display any fancy rotating objects. It merely projects the 3dimensional http://www.funet.fi/~msmakela/software/fractal/

Last essential modification: March 24, 1999 Marko Mäkelä 's software projects Mandelbrot and Julia fractals Fractals became popular in the 1980s, when microcomputers started to become common. Everyone could produce the Mandelbrot set with their home computer. It is difficult to conceive how so simple mathematic formulae can create such beautiful images having such detailed and in some sense recursive structure. Some theory The underlying mathematics makes use of complex numbers. For each point c=t+j x n the complex plane, one associates a colour by using an iterative process: z z (i+1) =z (i) ²+c The colour of the point c is the smallest i for which (i) This is the process for the Mandelbrot set. The Julia set is similar, but it uses the formulae z =c z (i+1) =z (i) ²+d Above, d is an additional parameter, which is used for all points in the fractal. Programming languages usually do not directly support complex number arithmetics. Therefore, the iteration equations are usually split into real and imaginary components z (i) =t (i) +j x (i) c (i) =ct (i) +j cx (i) and the iteration step is as follows: t (i+1) =t (i) ²-x (i) ²+ct x (i+1) =2 t (i) x (i) +cx This can be generalized to 3 dimensions by adding another coordinate y , which is orthogonal to both the t and x axes: t (i+1) =t (i) ²-x (i) ²-y (i) ²+ct x (i+1) =2 t (i) x (i) +cx y (i+1) =2 t (i) y (i) +cy These formulae were originally found out by my friend Topi Kärki, who wanted to see how the Mandelbrot fractal behaves when using quarternions instead of complex numbers. It turned out that the 4

45. Amazing Seattle Fractals! - Fractal Sites Benoit Mandelbrot a mathematician at IBM is credited with the paper complete with illustrations on HIGHER ORDER mandelbrot fractals EXPERIMENTS IN http://www.fractalarts.com/ASF/Fractalsites1.html

Amazing Seattle Fractals! Home Fractal Art Galleries Fractal Tutorials Fractal Of The Week ... About This is a list of previously profiled sites in "Fractal Art Sightings". Karma Storm Steve Bennett's site although not fractal related, has wonderfully created art animations worth checking out. Iterations Et Flarium24 Steven Ferguson's program Tiera-zon, used for most of the fractals on this site, may be found here but his fractal galleries are also well worth the visit. Fractals! Samuel Monnier's first caught my attention for his "Space" scenes created using Ultra Fractal. Be sure to check this one out! Fractal Dimentia Mark Townsend's site, featuring his fractal art using Ultra Fractal, has some very nice fractals. Fractal Movie Archive Kevin Adams' site features animations and zooms of fractals in several different formats such as .avi, Quicktime etc. Animated Fractals Alden Bliss's site has a number of good demonstrations of fractal zooms, pallette animations and "Lake" fractals ( a java application ). "Monsters and Strange Creatures" galleries by Jos Ley has some fun (and very good!) fractal art. These fractals are open to the imagination but definitely resemble strange creatures! Check it out!

46. • Pocket PC For All › Software Detail PocketFract is a Mandelbrot set generator for Pocket PC. You can design mandelbrot fractals, alter them and redraw them just by tapping the screen with your http://www.ppc4all.com/appdetail.php?id=1061

47. 6.170 Lab 6: Performance, Profiling, And Tuning Mandelbrot.java uses ComplexNumber s to compute mandelbrot fractals. MandelView.java displays mandelbrot fractals; this is the class you must run to http://6170.lcs.mit.edu/www-archive/Old-2003-Spring/labs/lab6/lab6.html

Laboratory in Software Engineering Spring 2003 Lab 6: Performance, Profiling, and Tuning Handout B6 Contents: Purpose Setup When to Optimize Code Profiling ... Further Reading Students completing the checkpoint for ps6 are only required to complete Exercise 4. You should read through the profiling sections if you are not sure how to profile your system. Purpose This lab will teach you some simple techniques for analyzing and improving the performance of your Java programs; you may find this topic useful in completing Problem Set 6. When you finish this lab, you should be able to: measure the running time and memory usage of Java programs identify common efficiency problems in Java solve these problems using optimizations There are three exercises in this lab which use a fractal generator to demonstrate good optimization practices. We provide you with the following source files and their Javadoc specifications ComplexNumber.java encapsulates a complex number. You will need to modify this file to solve Exercise 2 Mandelbrot.java uses ComplexNumber s to compute Mandelbrot fractals. You need to modify this file to solve all of the exercises.

48. Welcome To The Fractal EXtreme Web Site Win32 shareware program for exploration of the mandelbrot set and other fractals. http://www.cygnus-software.com/

Fractal eXtreme News: December 2003 a bug fix version of Fractal eXtreme was released. As usual this is a free upgrade for registered customers. November 2003 a bug fix version of Fractal eXtreme was released. As usual this is a free upgrade for registered customers. October 2003 a new version of Fractal eXtreme was released. As usual this is a free upgrade for registered customers. February 2002 a bug fix version of Fractal eXtreme was released. November 2001 a brand new version of Fractal eXtreme was released. This new version has many new features, including antialiased fractals and zoom movies, and an improved way of purchasing Fractal eXtreme January 1, 2001 Improved zoom movie player now has OpenGL support for vastly improved animation quality and much higher frame rates. Download the new zoom movie player here or download all of Fractal eXtreme here Sep 11, 1999 Improved zoom movie player now has colour cycling and .avi frame rate specification. Download the new zoom movie player here or download all of Fractal eXtreme here March 19, 1998

49. Efg's Fractals And Chaos Page Software and information resource on the mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds. http://www.efg2.com/Lab/FractalsAndChaos

Contents Fractals Chaos Glynn Function Gallery Also see the Fractals and Chaos Section of the Math Reference Library in look for Mathematics Fractals / Chaos Note: If you have a fast machine (233 MHz Pentium II or faster), you'll likely need a patch to run TP 7 programs on this page. See this fix for "Runtime Error 200." Fractals Program Description Files Keywords Tutorial about Mandelbrot and Julia sets. Mandelbrot Set, Julia Set Evolution of the MandelbrotSet Mandelbrot Set Fractal Discovery Lab Art Gallery, Microscope, Movies, Tools, Library Fractals Show 2 Fractals, Chaos, Mandelbrot Set, Julia Set, Biomorph, Rainbow, WavelengthToRGB, pf32bit, Delphi Sierpinski Triangle Gasket Sierpinski triangle, Sierpinski gasket, fractals, self-similarity, Hausdorff dimension, digital pantograph, world-to-pixel mapping, recursion von Koch Snowflake von Koch curve, von Koch snowflake, fractals, self-similarity, Hausdorff dimension, digital pantograph, world-to-pixel mapping, recursion Chaos Program Description Files Keywords Iterated Function System to create four ferns (Also see, Mathematical Recreations

50. Fractal Explorer Program that can generate polynomial and iteration sets as mandelbrot, Julia, Newton like fractals and orbital fractals. http://www.eclectasy.com/Fractal-Explorer/index.html

Fractal Explorer Fractal Explorer Fractal Explorer Fractal Explorer Home License What's new Download ... Caricatures since Dec 24, 1998 Fractal Explorer is a freeware fractal generator that can produce mysterious and beautiful mathematically-based images. Not just a tool for professionals, FE can provide hours of entertainment for beginners and experts alike ! Fractal Explorer can render the classical polinomial fractal sets (like the Mandelbrot-set, the Julia-set, the Newton-set and theirs variations), 4D-complex fractals (called «quaternions»), 3D «strange» attractors, and IFS. Also, FE has many features for creation of special effects and improvement of the pictures. We are sorry because of absence of the Help file, but simple user-friendly interface should not cause difficulties. Thanks for your interest in this software, we hope you enjoy it ! Site news: January 2005 Fractal Explorer 2.02 has been released. Welcome to the download page!

51. Fractals [encyclopedia] Click here for customer reviews/more info on fractals, Googols and Other mandelbrot, who is often called the father of fractals, investigated the http://kosmoi.com/Science/Mathematics/Fractals/

EncycloZine Astronomy Biology Chemistry ... The Misbehavior of Markets Benoit Mandelbrot, Richard L. Hudson Fractals, Googols and Other Mathematical Tales Theoni Pappas The Fractal Geometry of Nature Benoit B. Mandelbrot The Computational Beauty of Nature: Computer Explo... Gary William Flake Trading Chaos : Maximize Profits with Proven Techn... Justine Gregory-Williams, Bill M. Williams Trading Chaos : Applying Expert Techniques to Maxi... Bill M. Williams Fractals and Scaling In Finance R.E. Gomory, Benoit B. Mandelbrot, P.H. Cootner, E.F. Fama, W.S. Morris, H.M. Taylor Fractals John Briggs Beauty of Fractals: Images of Complex Dynamical Sy... Heinz-Otto Peitgen The Fractal Murders (Pepper Keane Mysteries) Mark Cohen Fractals Kosmoi.com Science Mathematics Fractals ... Pictures Sierpinski Triangle In mathematics , a class of complex geometric shapes that commonly exhibit the property of self-similarity, such that a small portion of it can be viewed as a reduced scale replica of the whole. The term fractal is derived from the Latin word fractus ("fragmented," or "broken"). Fractals are distinct from the simple figures of classical, or Euclidean geometry . (the square, the triangle, the circle, the sphere, etc.) They are capable of describing the many irregularly shaped objects or spatially nonuniform phenomena in nature that cannot be accommodated by Euclidean geometry.

52. M3DSaver Windows screensaver featuring 3D images, and fractals using mandelbrot and Julia Set. Download demo version. http://m3dsaver.netfirms.com/

53. 3D Fractals Resource on the bicomplex generalization of the mandelbrot set. Includes scientific publications, illustrations, news and downloads. http://www.3dfractals.com/

54. Fracture : A Fractal Screensaver Fracture is a screensaver for Mac OS X that can generate a wide variety of fractal images, including the mandelbrot Set, Julia sets, SelfSquared Dragons, and Attraction Basin fractals. http://www.sticksoftware.com/software/Fracture.html

Fracture 1.2 : A fractal screensaver Download Fracture (276K) VersionTracker's Page on Fracture Price: $10 ( Kagi PayPal Fracture is a screensaver for OS X that creates a wide variety of fractal images. It can render the Mandelbrot Set, Julia Sets, Self-Squared Dragons, and Attraction Basin fractals generated using Newton's Method, Halley's Method, and two other root-finding algorithms. It can make images using advanced fractal imaging techniques like orbit traps, periodicity analysis, and binary decomposition, and it can use several different parameterizations for even greater image variety. Here's one sample image (visit Stick Software's gallery to see more): It will use multiple processors if you have them, to make its calculations faster, and it will display fractals on multiple monitors if you have them (we have a photo that user Aneel Nazareth sent us of Fracture running on five screens at once , in fact). It can generate a wide variety of color schemes under user control. And it can even antialias its images, for the maximum in image quality! It can be controlled by the user while it is running, so you can find a color scheme you like, skip images you don't like, hold images you do like, and save images you particularly like to disk. As you can rely on with Stick Software products, it has a suitably overengineered configuration panel that lets you control many details of its operation. Here's a snapshot of one tab of that panel:

55. Fractal Explorer: Mandelbrot And Julia Sets (by Fabio Cesari) Keywords fractals, mandelbrot set, fractal, julia sets, quaternion, quaternion julia sets, mandelbrot, Julia. Your browser doesn t support frames. http://www.geocities.com/CapeCanaveral/2854/

Keywords: fractals, mandelbrot set, fractal, julia sets, quaternion, quaternion julia sets, Mandelbrot, Julia Your browser doesn't support frames. This site is best viewed with , or an equivalent browser that supports JavaScript and frames You can always access this no-frames version of this site. If you have troubles accessing it, please let me know Many people have probably been fascinated by the infinite complexity and beauty of fractals. I wrote this brief tutorial to explain, in simple terms, how the Mandelbrot set and Julia sets are generated. This document provides an informal introduction to these subjects, and is only intended to be a starting point to learn more about fractals and fractal geometry. You can contribute to the future development of this site by filling out the feedback form Comments and suggestions are very appreciated. Have fun! About complex numbers Mandelbrot set Julia sets Images gallery ... Quaternion Julia sets images gallery" Other pages: About the author Links Feedback form Sign my guestbook ... View my guestbook This page hosted by Get your own Free Home Page

56. Fractal Screensaver - Fractal Geometry Art - GEOSS Screensaver for Microsoft Windows featuring Julia and mandelbrot sets, dynamic systems, stereograms, automatons and Lsystems. Includes basics, sample computer code and contact. http://www.canadasmountains.com/fractals/geoss/index.htm

GEOSS Fractal Geometry What The Heck? Instructions Fractal Descriptions Chaos Crystals Dynamic FractalGrams ... Twist Appendix Further Reading Downloads Sample Program System Requirements ... Contact GEOSS: A Fractal Geometry Screensaver A mostly non-Euclidean screen saver. Overview GEOSS The Geometry Screensaver for Microsoft Windows - A set of Fractal Screensavers for Windows that provide endless variety. The programs provide password protection and selectable options to adjust the output to your liking. Explore the worlds of the Julia and Mandelbrot sets, dynamic systems, 3d stereograms, automatons, L-systems and more. Version 1.0.1 var sc_project=209859; All rights of reproduction in other media reserved.

57. Fractal Solution Take the most famous of all fractals the socalled mandelbrot Set, named after IBM mathematician Benoit mandelbrot. Sometimes described as the most http://www.geocities.com/Omegaman_UK/fractal.html

Mathematics Finding the fractal solution Fractals are the abstract made gloriously visible. And now they're becoming useful shrinking images,diagnosing madness,even finding gold. It turns out that fractals are the very stuff of the universe Naming the abstract: Benoit Mandelbrot The man who lent his name to the most familiar of all fractals - the Mandeldbrot set - is a 70-year-old French mathematician and information theorist. He published his first work on fractals in 1977;the Set's subsequent popularity catapulted Mandelbrot from obscurity to international fame A couple of years ago they were merely a craze, appearing everywhere from art galleries to T-shirts. Their intricate multicoloured whorls and spikes, at once bizarre yet strangely familiar, adorned album covers, posters and book jackets. These extraordinary images were fractals, patterns within patterns within patterns, ad infinitum. They inspired artists to create images of alien landscapes and sent mathematicians soaring into exotic flights of theory to uncover their secrets and ramifications. But now they are much more than just a buzzword for a bizarre abstract image. Their unique properties are being put to use in an astonishing range of applications.

58. Don Archer Digital Art Traditional fractals, music, fractals combined with verse. Photo of Benoit mandelbrot taken April 6, 2001. http://www.donarcher.com/

Friday, 9/23/2005 , 1:39:37 PM ET, Brooklyn and Prattsville, NY Updated September 21, 2005 This site is an exercise in love, vanity and art. It includes my current images, vintage fractals, animations, fractal music, ceramic tiles, digital photographs, digital postcards, and more... There are 3 viewers online now. Enjoy! And thanks for visiting! COLLECTION 2004 Gallery I December 2004 Gallery II Oct-Nov 2004 ... January-June 2004 COLLECTION 2003 Gallery I January-June 2003 Gallery II July-December 2003 COLLECTION 2002 Gallery I January-June 2002 Gallery II July-December 2002 ... VERSE VINTAGE FRACTALS Fractal Zoo, Part 1 Fractal Zoo, Part 2 Fractal Camera Black and white ... Faultline fractals COLLECTION 2005 In Retrospect August 2005 Theme and Variations June-July 2005 ... April 2005 Virtual Portraits March 2005 February 2005 HTML FORMAT FLASH SLIDESHOW January 2005 HTML FORMAT FLASH SLIDESHOW COLOR SHIFT ANIMATIONS Don Archer, director CREDITS Online ABS gallery 2001-2003 crowns me "fractal guru" and publishes comprehensive exhibit of my art. Print art included in the collection of Ball State University Art Museum, Muncie, IN.

59. Benoit Mandelbrot, Fractals And Astronomy (Part 1) Benoit mandelbrot, fractals and Astronomy (Part 1) http://www.umich.edu/~lowbrows/reflections/1998/dsnyder.3.html

Benoit Mandelbrot, Fractals and Astronomy (Part 1) by Dave Snyder Printed in Reflections: November, 1998. Fractals are mathematical objects with strange properties. They have been known for many years, but had been relegated to an obscure corner of mathematics. In the beginning fractals were curiosities, very few people thought they had any real applications (Ludwig Boltzmann and Jean Perrin were among the exceptions). All that changed when Benoit Mandelbrot began his career. Mandelbrot discovered that complex phenomenon in a variety of sciences, including astronomy, could be understood in terms of fractals. Fractal geometry along with several other sciences were motivated by examining human senses. For example, the sense of sight led to the study of electromagnetic radiation and the sense of hearing led to the study of acoustics. However until recently, there had never been any science of roughness. I must make this clear, the orbits of the planets are not fractals: they are very close to perfect ellipses. However if we plot the predicted positions of a particular planet under a number of conditions we find they all fit within a boundary curve called the basin of attraction. This basin is often a fractal. As an aside, many of these fractals have been used to produce computer images, some of which are quite beautiful. These images are typically very colorful and have caught the attention of some artists. Note that the images are usually based on black and white fractals, the colors are simply added by the computer. While these images have played an important role in making non-specialists aware of the subject, computers played very little role in the development of fractal geometry.

60. Chaos Theory And Fractals Benoit mandelbrot believed that fractals were found nearly everywhere in nature, When changing the values for the mandelbrot fractal set from lines to http://www.mathjmendl.org/chaos/

Chaos Theory and Fractals By Jonathan Mendelson and Elana Blumenthal Outline Introduction to Chaos Determinism Early Chaos Edward Lorenz ... Works Cited Introduction to Chaos The dictionary definition of chaos is turmoil, turbulence, primordial abyss, and undesired randomness, but scientists will tell you that chaos is something extremely sensitive to initial conditions. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. A chaotic system can actually develop in a way that appears very smooth and ordered. Determinism Determinism is the belief that every action is the result of preceding actions. It began as a philosophical belief in Ancient Greece thousands of years ago and was introduced into science around 1500 A.D. with the idea that cause and effect rules govern science. Sir Isaac Newton was closely associated with the establishment of determinism in modern science. His laws were able to predict systems very accurately. They were deterministic at their core because they implied that everything that would occur would be based entirely on what happened right before. The Newtonian model of the universe is often depicted as a billiard game in which the outcome unfolds mathematically from the initial conditions in a pre-determined fashion, like a movie that can be run forwards or backwards in time. Determinism remains as one of the more important concepts of physical science today. Early Chaos Ilya Prigogine showed that complex structures could come from simpler ones. This is like order coming from chaos. Henry Adams previously described this with his quote "Chaos often breeds life, when order breeds habit". Henri Poincaré was really the "Father of Chaos [Theory]," however. The planet Neptune was discovered in 1846 and had been predicted from the observation of deviations in Uranus' orbit. King Oscar II of Norway was willing to give a prize to anyone who could prove or disprove that the solar system was stable. Poincaré offered his solution, but when a friend found an error in his calculations, the prize was taken away until he could come up with a new solution that worked. He found that there was no solution. Not even Sir Isaac Newton's laws provided a solution to this huge problem. Poincaré had been trying to find order in a system where there was none to be found.

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