41. Fractals Create Some Fractal music. Visit Fractal music to begin learning about fractalmusic. More Fractal Websites; Fractal music The Sound of Chaos http://42explore.com/fractal.htm

The Topic: Fractals Easier - A fractal is a shape, often drawn by a computer, that repeats itself in a pattern. The design shapes usually reoccur in different sizes. Harder - Fractals are endlessly repeating patterns that vary according to a set formula, a mixture of art and geometry. 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. You can see countless variations of the same pattern emerge in the crystals over time. Exploring Fractals (Grades 9-12) by M.A. Connors http://www.math.umass.edu/~mconnors/fractal/fractal.html This website explores fractal dimensions of strictly self-similar fractals, from Cantor Dust to the Fractal Skewed Web. Includes a teacher information section. Related Websites: 2) Fract-ED (Grades 8 and Above) http://www.ealnet.com/ealsoft/fracted.htm

42. File Library At Channel 1: Fractals 45799, 1118-93, The Well Tempered Fractal v2.0 - an interactive fractal musicgenerator. Generates musical melodies by mapping fractals to music. http://www.filelibrary.com/Contents/DOS/94/14.html

First Shareware Hall of Fame Award Winner June 1997! New Files Top 20 File Search Message Board F ractals: files Search for concept filenames only Jump to files beginning with: A B C D ... Z Jump to page number NEW this page Filename (click to download) Size Date Description wtf20.zip The Well Tempered Fractal v2.0 - an interactive fractal music generator. Generates musical melodies by mapping fractals to music. Four fractal types, twenty-one scale types and twenty symmetry operators. Remap, change symmetries, change fractal types on the fly. xaos12b.zip xaos12s.zip xaos21b.zip xaos21s.zip ... xaos21_o.zip XaoS is a fast portable real-time interactive fractal zoomer. xmt2.jpg Fractal landscapes - K/Q 4/3 xmt3.jpg Fractal landscapes - K/Q 4/3 xmt4.jpg Fractal landscapes - K/Q 4/3 xmt5.jpg Fractal landscapes - K/Q 4/3 xmt6.jpg Fractal landscapes - K/Q 4/3 xmt7.jpg Fractal landscapes - K/Q 4/3 xmt8.jpg Fractal landscapes - K/Q 4/3 xmt9.jpg Fractal landscapes - K/Q 4/3 yank42b.zip Yankovic 4.2b, generates Yankovic set, a fractal unavailable in any other software. This is a special edition version before the release of Yankovic 5.0. yuvpak2.zip

43. The Chaos Metalink -- Featured Sites Don Archer s Fractal Art, music and Udraw fractals Site Learn how fractalmusic is made, hear examples and make some of your own! http://www.industrialstreet.net/chaosmetalink/LiveSites.asp?CategoryID=4

44. Fractal Music Contains several galleries of fractal images, wallpapers, fractal music, anddiscussions on fractals as art. It also includes an extensive upto-date list http://www.fractovia.org/fmusic/

t h i r d . a p e x . t o . f r a c t o v i a NAVIGATE en-trance home galleries wallpapers ... portal VISIT... Fractovia's Discussion Board now back online. Participate. Fractal Compositions Elkie's Child Dexia Mandelbrot Trabalg ... Voicez These are my first experiments with fractal music. They were created with sevaral freeware fractal music genertors, mainly Musinum, Mandelbrot Music, and LMUSe (for more information visit the Software section). The files are only available in 128 and 64 kbps MP3 format (the former is highly recommended), although the original files were recorded as MIDI files. "Star Names" was part of the "Automated Compositions" series. It isn't fractal music in essence, but randomly produced music generated with predefined parameters and styles, using the Automated Composing System, (Tetsuji Katsuda's Music Laboratory ). Some styles were modified to produce the "beta" version of this file, and later "post processed" with several freeware MIDI editors and sequencers to get the results you should expect to hear. The sample is only available as 128 kbps mp3 file. About MIDI files The sound reproduction of MIDI files may vary from system to system depending on the MIDI driver and sound card on each computer. Thus, your computer will render them according to the hardware it has to interpret MIDI instructions. I have tested them in various environments, and each played a somewhat different melody.

45. Blazingfire Cards A collection of illustrations and photographs featuring angels, dragons, fantasia, fractals, kaleidoscopes as well as birthdays, love and sympathy. Includes selection of poems, music, java effects and backgrounds. http://blazingfire.net/Home.html

Bookmark This Page Number of visitors to our site Page Counter Please vote for our site at these spots. Need help setting up your site? Click Here Today's Newsletter ~View/Sign my guest book here~ Contact Us Send a Card Card of the Day Waterfall Cards ... FREE referral system If you would like to have a website, but don't know how to go about setting things up, I can help you with it for a reasonable fee of $50.00 per page. If you are interested just send me an email. E Mail Me Back to top Compliments of

46. Fractal Music But why even attempt fractal art and music? What relevance do fractals have to The application of fractals in music may seem a bit odd at first, http://www.unc.edu/~jimlee/JohnObrienFractalMusic.htm

Fractals and Their Use in Music Comm 141 John O’Brien Two years ago, at a summer electronic music workshop at Oberlin College in Ohio, I was presented with some of the most intriguing music I have ever heard. Initially, the music sounded like nothing more than noise, random short bleeps with no clear purpose or arrangement. I could not help but wonder why anyone would want to hear this ‘music’ and dismissed it as a failed attempt by someone wanting to be avant-garde simply for the sake of being avant-garde. I could not have been more wrong. A few days later I had the opportunity to hear another piece, The Voyage of the Golah Iota explained by its composer, Gary Nelson. While the music did not sound any better to me aesthetically at the time, I began to understand the reasons behind it and the concepts it worked under. Since that time I have come to learn more about this incredible method of writing music, and in the process have begun to develop an aesthetic taste for the music The music I am talking about is fractal music. Fractal music is based upon the mathematical concept of the fractal.

47. Mathematics Archives - Topics In Mathematics - Fractals KEYWORDS Tutorials, Gallery, Fractal music, Bibliography, Software, Newsgroups;FractED ADD. KEYWORDS Iteration, Attractor, Software, Tutorial, http://archives.math.utk.edu/topics/fractals.html

Topics in Mathematics Fractals Chaos, Fractals, and Arcadia ADD. KEYWORDS: The Chaos Game, The Sierpinski Hexagon, Iterated Function Systems Chaos in the Classroom, Boston University ADD. KEYWORDS: The Chaos Game, Self-similarity, Fractal Dimension, Iterated Function Systems Clifford A. Pickover's Homepage ADD. KEYWORDS: Cellular Automata, Carotid-Kundalini Functions, Books, Puzzles, JAVA Geometry Explorer The Dance of Chance ADD. KEYWORDS: Random Processes, Branching Structures, Patterns in Nature, Student Activities, Laboratory Experiments, Visualization, Software, Fractal Dimension, Fractal Coastlines Diffusion-limited Aggregation Exploring Fractals ADD. KEYWORDS: Lesson Plan, Tutorial, Bibliography Fantastic Fractals ADD. KEYWORDS: Tutorials, Gallery, Fractal Music, Bibliography, Software, Newsgroups Fract-ED ADD. KEYWORDS: Iteration, Attractor, Software, Tutorial, Bifurcation, Self-similarity, Strange attractor Fractal Clouds The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs

48. Mathematics Archives - Topics In Mathematics - Art & Music KEYWORDS fractals, Feedback and Chaos, Sonic and Visual Art Maple;fractals Calendar The Golden Section in Art, Architecture and music http://archives.math.utk.edu/topics/artMusic.html

Topics in Mathematics ArtByMath ADD. KEYWORDS: Fractals Artlandia ADD. KEYWORDS: Software, Mathematica, fractals, randomness, symmetry, kaleidoscopic patterns ArtMath Transformations ADD. KEYWORDS: Symmetry, Escher, Combining Transformations, Worksheets, Groups Contours of the Mind ADD. KEYWORDS: Fractals, Feedback and Chaos, Sonic and Visual Art Did Mozart Use the Golden Section? Escher's World ADD. KEYWORDS: Pedagogy Fourier Approximations and Music ADD. KEYWORDS: Supplementary Materials, Maple Fractals Calendar The Golden Section in Art, Architecture and Music ADD. KEYWORDS: Fibonacci Numbers, Golden ratio, History Grammar-Based Music Composition Hop's Escher Tiles ISAMA - The International Society for the Arts, Mathematics, and Architecture ADD. KEYWORDS: Architecture, Books and Videos, Computer Graphics, Literary Arts, Mathematics Web Resources, Mathematical Modeling Kits, Mathematical Visualization, Music and Dance, Online Journals, Paintings and Prints, Polyhedra, Related Organizations, Sculpture, Teaching, Tesselations and Tilings Java Geometry Explorer ADD. KEYWORDS:

49. Fractal Links - Amazing Seattle Fractals! Fractal music Lab Fractal music Software, Fractal Museum Store Fractal art,gifts etc. The Fractal music Forum Fractal music EGroup http://www.fractalarts.com/ASF/Fractal_Links.html

Amazing Seattle Fractals! Home Fractal Art Galleries Fractal Tutorials Fractal Of The Week ... About Fractal Links I've included many resources on this page if you are looking for more information on fractals, including other fractal artists, tutorials or more information about fractals in general. If you are looking for fractal software programs check out my software page. Enjoy! Seattle Fractals Digital Art If you are interested in any of my art prints or downloading any of my screensavers for a free evaluation, you can find them here. High resolution art prints, fractal art galleries, fractal screensavers, custom made to order screensavers and more! Link Spectrum Fractal Tutorials and Related Links Fractal Types Explantions and illustrations of various types of fractals. UF Spiral Tutorial Dr. Joseph Trotsky's excellent tutorial on creating the classic fractal spiral form as well as other helpful UF info. He has also written helpful info on the program Fractal Explorer. Janet Parke Preslar's excellent tutorials on using the Ultra Fractal Program. Prof. John Matthew's

50. [ Wu :: Fractals ] fractals can even be used to make music! if you think of music as a sequence ofamplitudes values over time, one could imagine constructing a sequence such http://www.ocf.berkeley.edu/~wwu/fractals/fractals.html

FRACTALS an introduction to fractals. topics discussed include fractals in nature and industry, and the basic mathematics behind generating several classic structures, including the mandelbrot set and sierpinski triangle. also included is a gallery of choice fractal art, including a few pieces made by myself. Fractal Intro Mandelbrot Sierpinski Gallery ... Return to Homepage A Short And Entertaining Introduction to Fractals a fractal is a geometric shape that can subdivided into parts, each of which is a reduced-size copy of the whole. the term was coined in the 1960s by benoit mandelbrot, a mathematician at IBM who adapted it from the latin adjective fractus , meaning "fragmented." to get a feel for what a fractal is, imagine inspecting a long, craggly, leafless tree branch on a frosty winter day. as your eyes scan the branch from its base to its tips, you notice that many sub-branches are generated along the way, and each sub-branch has a structure symmetric to the original, but smaller in scale. these sub-branches in turn fork off self-symmetric branches of their own. in the purest sense of a fractal, we imagine this branching process as never ending. you could compare it to the effect produced when two mirrors are faced toward each other, producing a claustrophobic, tunnel-like view of infinite imitation at smaller and smaller scales. a nice example of this is seen in the mandelbrot fractal at left, designed by Paul deCelle. usually one's first response to fractals is simply this: they are beautiful! indeed, they are visually arresting, and there are many reasons why. perhaps one reason is that they exhibit extreme levels of

51. Mathematics Magazine: Music And Mathematics: From Pythagoras To Fractals music and Mathematics From Pythagoras to fractals, Oxford University Press,2003; vi + 189 pp, $74.50. ISBN 019-851187-6. http://www.findarticles.com/p/articles/mi_qa3789/is_200404/ai_n9401277

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Home Advanced Search IN free articles only all articles this publication Automotive Sports FindArticles Mathematics Magazine Apr 2004 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports Music and Mathematics: From Pythagoras to Fractals Mathematics Magazine Apr 2004 by Campbell, Paul J Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. Fauvel, John, Raymond Flood, and Robin Wilson (eds.), Music and Mathematics: From Pythagoras to Fractals, Oxford University Press, 2003; vi + 189 pp, $74.50. ISBN 0-19-851187-6. The 10 essays here treat tuning and temperament, Kepler's cosmology, the science of musical sound, the spacing of frets on stringed instruments, Helmholtz's physiological basis for music, frieze patterns in music, change ringing, mathematical ideas in composition, projective planes and the 7-tone system, and composing with fractals. Continue article Advertisement Save Print Send Link ... Subscribe IN free articles only all articles this publication Automotive Sports About Us Terms of Service Advertise with Us LookSmart Solutions: FindArticles Furl.net

52. John Luther Adams: Writings In that spirit, I began my investigation of fractals as music with the simplestof forms the so called classical fractals, created by linear, http://www.johnlutheradams.com/writings/noise.html

"Nothing essential happens in the absence of noise... in most cultures, the theme of noise lies at the origin of the religious idea... Music, then, constitutes communication with this primordial, threatening noise prayer." Jacques Attali My music has long been grounded in the physical, cultural and spiritual landscapes of the North and in an ideal of sonic geography place as music, and music as place. More recently, I've begun to explore new aspects of the relationships between music and place, in a convergence of sonic geography with sonic geometry. We often think of music as a kind of language, which of course it can well be. But rather than a music of discourse, mine is a music of the sounding image. My concern is not with musical "ideas" and the rhetoric of composition, but with the singular sonority that sound which stands for nothing other than itself, filling time and space with the vivid, physical presence of a place. For many years now, I've listened carefully to the sounds of the natural world and attempted to translate what I've heard there into my own music. Initially, I was attracted to the songs of birds and other more "poetic" dimensions of the soundscape. But gradually, I've been drawn to the "noiser" sounds of nature ocean waves and waterfalls, storm winds and thunder, glaciers crashing into the sea those elemental voices which resonate so profoundly in the human mind and spirit.

53. Chaos Report - Heather Elko It does not have the colors that would allow fractal music to be created. And interestingly, when most fractals are converted to music, they are found http://pear.math.pitt.edu/mathzilla/Examples/chaos/studentReports/HeatherElko.ht

Chaos start page Heather Elko Chaos and the Logistic Map February 2001 Full Report (MS Word document) Chaotic Music Fractals are applications of chaos theory. They are derived by entering an equation into a computer. The picture that results, while seemingly chaotic, actually repeats over and over within itself. Thus, chaos theory emerges, which shows that seemingly chaotic systems actually do have order. These fractals are important because they are found over and over throughout nature. Coastlines have been described as chaotic, as they can be analyzed on many different levels producing different results. A coastline can be analyzed on the astronomic, topographic, or even microscopic level, each producing very different results. Fractals can also be seen in plants such as the fern, which is found to repeat itself over and over. Michaech is found to repeat itself over and over. Michael Barnsley was able to create a fractal that looked extremely similar to a fern. But one of the most interesting uses of fractals that I have discovered is that they are being used to create music. Music from chaos. Music from an algorithm. It's extremely compelling. There are many different types of fractals, and thus many different ways to transfer them to music. One example is the Julia set, below.

54. Psynews.org V/A - Out On The Full These tracks are as random as fractals. Psychedelic music is about being in themoment and expecting the unexpected. Psychedelic music should question the http://www.psynews.org/forums/lofiversion/index.php?t22032.html

55. Fractals Tag Search Results - Shadows.com fractals search results on Shadows.com. Find, tag, comment and rate Read whatpeople are saying about fractals. fractals, music. Search Google http://www.shadows.com/tags/fractals music

Welcome to Shadows create an account help log in Tag: fractals music Search Google Narrow Results: baddesign cool mandelbrot maths ... clear tags Top Users of this Tag: tagcrawler My results Please Log in to see items you have tagged. What is Shadows? Shadows is a community based service that gives you the power to create your own search engine, find sites that interest you, and share your entire Internet experience with anyone on the web. Learn More -> Click here to quickly begin using tags, comments, and ratings. Community Results Sort by: most tags most recent Displaying 1 to 2 of 2 results The Self-Similar Guns N' Roses Midi Synth !!! -... 1 users - Last action 6/17/2005 by tagcrawler Tagged as: music fractals baddesign selfsimilargnr.com/index.htm ... View Shadow page 1 users - Last action 6/17/2005 by tagcrawler Tagged as: music maths mandelbrot fractals ... View Shadow page google_ad_client = "pub-3706667038051159"; google_ad_width = 160; google_ad_height = 600; google_ad_format = "160x600_as"; google_ad_channel = "2160280290"; google_page_url = "http://www.google.com/search?q=fractals music"; google_color_border = "FFFCF8"; google_color_bg = "FFFCF8"; google_color_link = "CC9900"; google_color_url = "CC9900"; google_color_text = "000000"; What Is Shadows?

56. Music Composition With Algorithms: Links fractals. The Fractal music Project (ClausDieter Schulz); Genetic SpectrumModeling Program / Fractal Melody Generator (R. Jurgens) http://www.msu.edu/user/sullivan/CmusAlgoLinks.html

Composition With Algorithms: Links Chaos Chua's Ossilator (Insook Choi, Robin Bargar, etc. Chaosynth: A Cellular Automata-based Granular Synthesizer (Eduardo Reck Miranda) Fractals The Fractal Music Project (Claus-Dieter Schulz) Genetic Spectrum Modeling Program / Fractal Melody Generator (R. Jurgens) Neural Nets, Cellular Automata Neural Network Music Composition by Prediction (Michael C. Mozer) Cellular Automata Tutorial (David G. Green) Cellular Automata Music (Eduardo Reck Miranda) Other Approaches Differential Equations and the Modelling of Musical Change Variations: Algorithmic Composition for Acoustic Instruments (Bruce L. Jacob) Recursion: A Paradigm for Future Music (N. Mucherino) Resources The Algorithmic Composition Homepage List of Tools for Algorithmic Composition (Amsterdam Catalogue of Compostion Algorithms) Algorithmic Composition As A Model Of Creativity (Bruce L. Jacob) Computer Music: Composition and Algorithms Scores and Analysis Cmus Resources CMusTutorials ... MSU CMus Studios Mark Sullivan : Courses Composition Computer Music Tangents ... Transients

57. Locating Books In Bailey/Howe Library (Math 17 : Applications Of Finite Mathemat Title music and mathematics from Pythagoras to fractals / edited by John Fauvel, Title, fractals in music introductory mathematics for musical http://bailey.uvm.edu/ref/patm/math17spring05bks.html

University of Vermont Bailey/Howe Library Information and Instruction Services Math 17 : Applications of Finite Mathematics Locating Books in Bailey/Howe Library The UVM Libraries Catalog http://voyager.uvm.edu/ Use the Library Catalog to locate books, journals ( not GUIDED KEYWORD SEARCH Guided Keyword broadens your search by looking for occurrences of words anywhere in the Library Catalog record. NOTE: Not all the books may be exactly what you are looking for. What is a Keyword search? Allows you to use your own words to construct a search. Searches for your search terms in all fields of the Library Catalog record. Search terms are highlighted in the record. Example Your topic is how music and mathematics are connected. Title: Music and mathematics : from Pythagoras to fractals / edited by John Fauvel, Raymond Flood and Robin Wilson. Published: Oxford ; New York : Oxford University Press, 2003. Description: 189 p. : ill., music ; 26 cm. Subject(s): Music Mathematics Collection: Bailey/Howe Books (3rd Floor) Call Number: Number of Items: Status: Not Charged Check Shelf Your keywords are: music, mathematics. Words like "connect" is implied.

58. The Well Tempered Fractal V3.0 - An Interactive Fractal Music The Well Tempered Fractal v3.0 an interactive fractal music generator.Generates musical melodies by mapping fractals to music. http://www.harmony-central.com/Software/Dos/welltemperedfractal.abs

The Well Tempered Fractal v3.0 - an interactive fractal music generator. Generates musical melodies by mapping fractals to music. Ten fractal types, twenty-one scale types and twenty symmetry operators. Remap, change symmetries and rhythms, change fractal types on the fly. Toggle between plain and textured images.

59. The Fractal Artists' Ring Hidden Dimension{;}A fractal art and music site in the Adirondacks{;}; Fractal VibesA site dedicated to the exploration of fractals in music and Art New http://www.ringsurf.com/netring?ring=Fractal_Art_Ring;id=28;action=next5

60. The Fractal Artists' Ring A site dedicated to the exploration of fractals in music and Art New Frontiers! some really cool fractal images and strange electronic music on one http://www.ringsurf.com/netring?ring=Fractal_Art_Ring;id=30;action=next5

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