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         Fractals & Music:     more detail
  1. Fractals in Music: Introductory Mathematics for Musical Analysis Second Edition (Inmusic) (Inmusic) (Inmusic) by Charles Madden, 2007-04-23
  2. Music and Mathematics: From Pythagoras to Fractals
  3. Fractal Music, Hypercards and More Mathematical Recreations from "Scientific American" by Martin Gardner, 1991-11-30
  4. Music And Mathematics: From Pythagoras To Fractals by Raymond Flood, Robin Wilson, Robin J. Wilson John Fauvel, 2003
  5. Formalised composition on the spectral and fractal trails (Skrifter fran Musikvetenskapliga institutionen, Goteborgs Universitet) by Magnus Eldenius, 1998

1. Don Archer Digital Art
It includes my current images, vintage fractals, animations, fractal music,ceramic tiles, digital photographs, digital postcards, and more
http://www.donarcher.com/
Wednesday, 6/9/2004 , 1:53:19 AM ET, Brooklyn and Prattsville, NY
Updated June 4, 2004 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 7 viewers online now. Enjoy!
And thanks for visiting! YEAR 2003
FRACTALS Gallery

December 2003
Gallery
November 2003
...
January 2003
YEAR 2002
FRACTALS Gallery

December 2002
Gallery November 2002 ... January 2002 YEAR 2001 FRACTALS Gallery December 2001 Gallery November 2001 ... Jan-April 2001 NEWEST IMAGES Gallery Stout Series Gallery Trichon Series ... Lake Series 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.
  • Some 180 fractals included in a CD-ROM, Fractal Frenzy II, Postcards from the Edge of Space, published 1995 by Walnut Creek.
  • Images included in Wirehead's CD-ROM, Virtual Media Gallery by Quantum Access, 1995.

2. Fractal Music Gallery
A collection of outstanding fractal and algorithmic music for online listening Welcome to the Fractal music Gallery. Here you can listen to outstanding examples of fractal and midi files derived from these fractals are sequenced by Don "The fractal
http://thinks.com/sounds/fractal.htm
Home Sounds
Fractal Music Gallery
Welcome to the Fractal Music Gallery. Here you can listen to outstanding examples of fractal and algorithmic music that we have collected for your delectation and edification.
Current guest artists are: Don Archer Phil Jackson Yo Kubota
Click. Listen. Marvel. Discover. Enjoy.
Images and midi sequences by Don Archer
Stonerli Haysjohn Makresne The fractal images are created with Fractint using parameters supplied by visitors to Don's U-draw facility, and the midi files derived from these fractals are sequenced by Don: "The fractal image is imported into the shareware program ART SONG, which scans the image for the RGB values of selected pixels, then converts these values into MIDI output. The MIDI file is then imported into a music sequencer, either Cakewalk and/or Orchestra Plus, where I try to identify and isolate melodic and rhythmic lines, reassign instruments, and put these lines or tracks together again in musically interesting ways. The creative work is largely in the sequencing." Visit Don Archer's Fractal Art and Music for further information and more examples.

3. MuSoft Builders: Creating Music Out Of Fractals With A Musical Generator
Create music out of fractals, numbers, your name or photo with a musical Generator a musical generator creates music out of fractals, numbers, text and graphics. The music can also be converted
http://www.musoft-builders.com/

Logo: Giaco Parkinson
Home Register Support ... Contact Welcome visitor
Welcome to MuSoft MuSoft is a developer of electronic composition, graphics and internet software. a Musical generator - creates music out of fractals, numbers, text and graphics. The music can also be converted to MIDI so that it can be played by other MIDI programs. A Musical Generator was chosen as product of the month in december 2002 and januari 2003 by the CNFractal Forum.
Click at the products below for a description, preview and download. a Musical Generator CamCapture Try the beta of a Musical Generator (Version 3.1) Version 3.0 of a Musical Generator has been released ... What is CamCapture 1.1? Both a Musical Generator and CamCapture have been awarded an editor pick from ZDNet (PC Magazine) . For their review of a Musical Generator click on the logo above. We have added a (in Dutch and English ). It has been reviewed in NRC Handelsblad (a Dutch newspaper). Home Register Support Contributions ... MuSoft

4. Sprott's Fractal Gallery
MIDI Fractal background music courtesy of Forrest Fang. Fractal of theDay. FRACTAL OF THE DAY. Every day at a few minutes past midnight
http://sprott.physics.wisc.edu/fractals.htm
Sprott's Fractal Gallery
Awards Received MIDI Fractal background music courtesy of Forrest Fang
Fractal of the Day
Every day at a few minutes past midnight (local Wisconsin time), a new 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 figure above is today's fractal displayed in low (320 x 200) resolution. Click on it or on any of the cases below to see them at higher (640 x 480) resolution with a code that identifies them according to a scheme described in the book. Older Fractals of the Day are saved in an archive , which you can access. If your browser supports Java, you might enjoy the applet that creates a new fractal image every five seconds or so. If you would like to place the Fractal of the Day on your Web page, you may do so provided you mention that it is from Sprott's Fractal Gallery and you provide a link back to this page.

5. The Sound Of Chaos
The sound of chaos This World Wide Web (WWW) site, part of the Discovery Channel Online, offers background on the how and why fractals can be used to make music and who is making this music along
http://rdre1.inktomi.com/click?u=http://www.discovery.com/stories/technology/fra

6. Fractals In Music
fractals In music. A project games). Chaos and fractals have alsobeen applied to music with varying degrees of success. fractals
http://www.cgl.uwaterloo.ca/~revane/chaos/main.html
Fractals In Music
A project by Edwin Vane (ID: 98237531) for Dr. Will Gilbert's course PMATH 370: Chaos and Fractals in the Faculty of Mathematics, University of Waterloo. Main Page White Music Brown Music 1/f Music Cantor Music ... Appendix
Abstract
This project will investigate several different methods for algorithmic composition of music. Three algorithms that produce music via random number methods are covered. These methods include White Music Brown Music , and 1/f Music . These methods are simple and produce only melodies. Two slightly more advanced algorithms are also considered for producing pleasing music where the purely random methods fail. These two algorithms include Cantor Music and IFS Accompaniment . These algorithms produce more complex (and pleasing) music with varying amounts of accompaniment and harmony.
Summary and Background
Chaos and Fractals appear in many forms throughout mathematics, art, and the world at large. Images of fractals (such as the one of the Mandelbrot Set to the right of the main title) are commonly known even outside the academic community. Fractals have been applied to image compression and to modelling real terrain in computer applications (for instance, fractal terrain generation in computer games). Chaos and Fractals have also been applied to music with varying degrees of success. Fractals, especially those generated via Iterated Function Systems, show varying degrees of self similarity. In the visual domain, this means that that the image of a fractal seen at one magnification is the same as the same fractal seen at a higher magnification (and perhaps at a different location). That is, fractals look the same close up as they do zoomed all the way out. A mountain looks (statistically) similar to a mound of dirt on the side of that mountain. A coast line seen from space looks (statistically) similar to that same coast line when viewed from a few feet away.

7. Fractals In Music
fractals In music. A project by Edwin Vane (ID 98237531) for Dr. WillGilbert s course PMATH 370 Chaos and fractals in the Faculty
http://www.cgl.uwaterloo.ca/~revane/chaos/brownMusic.html
Fractals In Music
A project by Edwin Vane (ID: 98237531) for Dr. Will Gilbert's course PMATH 370: Chaos and Fractals in the Faculty of Mathematics, University of Waterloo. Main Page White Music Brown Music 1/f Music Cantor Music IFS Accompaniment Appendix
Brown Music
Algorithm and Background
Brown Music is very similar to white music in that in involves choosing notes randomly. However, instead of choosing random notes from within a subset of possible playable notes, brown music is created by starting at a note and choosing random distances to move from that note. Directions can be up or down but distances are usually small. In the examples generated below, the maximum possible distance is 2 and the minimum distance is 0. The notion of distance is flexible as well. When dealing with strict scales, a distance of 1 can be interpreted as moving from one note in the scale to the next or previous. When dealing with chromatic scales, a distance of 1 can instead be one semi-tone. Notes are chosen from fixed scales in order to make brownian motion sound better. The chromatic scale is included here to demonstrate the effect of not imposing a scale on the choice of notes. In the following examples, a range of two octaves is used. If brownian motion of notes tries to move outside of the two octave range, the motion is rebounded off the sides in the opposite direciton. The notes are also assigned note lengths according to brownian motion. Notes are not allowed to get shorter than an eighth note or logner than a half note (.5 and 2 beats respectively) and the distance of 1 for note duration is one eighth note.

8. Fractals And Music
fractals and music Gustavo DiazJerez Electronic musician, Oct 1, 1999. You llalso find links to other fractal music software at that site.
http://emusician.com/ar/emusic_fractals_music/
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List Rentals

Fractals and Music
Gustavo Diaz-Jerez
Oct 1, 1999 12:00 PM
E-mail this article
Most musicians have seen fractal images-those hauntingly beautiful pictures generated through mathematical equations. But how many people are aware that the same equations can be used to create hauntingly beautiful music? This article will explore fractals and discuss how they can be employed in musical composition. The technique is so versatile that you can use it to create music in any style, and it has great potential for adding an exciting new element to your music. Studying music from a mathematical point of view is nothing new; it dates back to ancient Greece. Around the fifth century B.C., Pythagoras uncovered mathematical relationships in music, in which musical intervals are represented as ratios of whole numbers. For example, the interval of an octave would be represented in the Pythagorean system as a 2:1 ratio because the frequency of the higher pitch is twice that of the lower. By the same system, the interval of a fifth would be 3:2, a fourth 4:3, and so forth. Other systems relating music to math have been developed, mainly in the 20th century. Among the many examples are Joseph Schillinger's System of Musical Composition and a method of composition developed by Olivier Messiaen in the 1940s. The more recent discovery of fractals and particularly their link to music has opened a door to composers, behind which lies immense creative possibility.

9. Fractals And Music
Reprints EPrints. List Rentals. fractals and music. Gustavo Diaz-Jerez FROM fractals TO music The secret behind fractal music involves something that mathematicians call mapping
http://rdre1.inktomi.com/click?u=http://emusician.com/ar/emusic_fractals_music/&

10. Chaos And Fractals In Music
Chaos and fractals in music. 4/5/01. Click here to start. Table of Contents.Chaos and fractals in music. Introduction. musical Properties Used. Rhythm.
http://www.science-house.org/student/bw/chaos/music/
Chaos and Fractals in Music
Click here to start
Table of Contents
Chaos and Fractals in Music Introduction Musical Properties Used Rhythm ... Conclusions Author: Elizabeth Snoke Home Page: http://www.science-house.org/student/bw/chaos/ Download presentation source

11. Chaos Theory, Fractals, Animation, Music Videos As A Scientific Experiment In Li
A free educational science, music, arts and entertainment site where you can downloadfree music videos of fractals in MPEG, MPEG2, DVD, DivX/MPEG4, Microsoft
http://gawain.membrane.com/multimedia/classic_fractal_animation/
Fractal Animation Music Videos
These music videos are an experiment with extemporaneous music and the chaos theory.
Singles
Collections
More Chaos Extemporaneous Music
Sidd's Science Center
Multimedia Special Of The Moment
Local Multimedia
http://membrane.com/

12. Fractals Music CDs At Songsearch
Shopping for fractals music CDs is easy at Songsearch. We are an online music CD and movie DVD store offering over 500 000 music titles, including hardto-find CDs and imports. fractals music CDs
http://www.songsearch.com/title/f/fractals.html
Fractals music CDs at Songsearch
FRACTALS Music CDs, DVD Movies, Music Videos, Songs, and Song Titles Buy Fractals Music CDs Email this page to a friend Link To Us Shop for more music DVDs , and CDs To see an image of the CD cover or a song title listing, click on the album name. CDs Show All Fractals Ron Marvin
DEU Import CD: $25.99
Age Special Order
Catalog#:TCL198725H
Song Titles

13. ThinkQuest : Library : Fractals Unleashed
Applications of fractals. Fractal music. One of the behind fractalmusic. The music of fractals A small collection of fractal music.
http://library.thinkquest.org/26242/full/ap/ap9.html
Index Math Fractals
Fractals Unleashed
For centuries mathematicians rejected complex figures, leaving them under a single description: formless. For centuries geometry was unable to describe trees, landscapes, clouds, and coastlines. However, in the late 1970s a revolution of our perception of the world was brought by the work of Benoit Mandelbrot. He introduced and developed the theory of fractals figures that were truly able to describe these shapes. The theory was continued to be used in a variety of applications. Out website will show fractals importance in areas ranging from special TV effects to economy and biology. Besides applications it will contain a course on fractals, making the user familiar with topics of various difficulties. The website will have an enhanced section on generating fractals, and the user will have a chance to create fractals using a Java applet. Visit Site 1999 ThinkQuest Internet Challenge Languages English Students Mikhail Stuyvesant High School, Brooklyn, NY, United States Ming Jack Stuyvesant High School, Fresh Meadows, NY, United States

14. Unusual Music At Unusual Research
UNUSUAL music. The music of fractals. Fractal music has an organic qualitybecause it is an accurate aural representation of the natural world.
http://users1.ee.net/pmason/music.html
UNUSUAL MUSIC
The Music of Fractals
Fractal Music by Patricia Mason Impossible Voices strange.attractions The Work of Friends and Associates All of the music on Unusual Research is actually the musical representation of fractal equations. As you listen to the music you are hearing a fractal progression of notes. Fractal music has an organic quality because it is an accurate aural representation of the natural world. Fractal Music Composition
Phil Jackson
and Patricia Mason Unusual Research Main Page

15. Slashdot | Using Fractals To Classify Music
Using fractals To Classify music article related to music. Using fractals To Classify music. Posted by CmdrTaco on Fri Aug 04, '00 0818 AM on software that can classify music with fractals and make it easier to find
http://slashdot.org/articles/00/08/04/1249258.shtml
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Stories Old Stories Old Polls Topics Hall of Fame ... Awards Services Broadband Online Books PriceGrabber Product News ... IT Research Using Fractals To Classify Music Posted by CmdrTaco on Fri Aug 04, '00 08:18 AM from the not-just-for-pretty-pictures-any-more dept. Brian McLaughlin writes "A company is working on software that can classify music with fractals and make it easier to find the tunes you want on the Web. Apparently, one can detect the type of music (jazz, heavy-metal, in-between, etc.) by detecting fractal patterns in the music." I'm looking forward to the day when my music can be indexed and crossreferenced every which way: artist, tempo, year, style, similiarity, heck I wanna know when the Beastie Boys sample The Beatles and be notified and give the option to follow up on the samples within the songs. Someday... I hope. Slashdot Login Nickname: Password: Create a new account Related Links
  • Brian McLaughlin classify music with fractals More on Music Also by CmdrTaco
  • This discussion has been archived. No new comments can be posted.

    16. Unusual Music Friends And Associates
    The Work of Friends and Associates. Fractal music Lab Experiments in Fractalmusic Composition. Don Archer s Fractal Art And music And UDraw fractals.
    http://users1.ee.net/pmason/music5.html
    UNUSUAL MUSIC
    The Work of Friends and Associates
    Fractal Music Lab:
    Experiments in Fractal Music Composition
    David T. Strohbeen's web site covering fractal-based music composition methods. Here you will find fractal music tools and fractal music files. For even more chaos in your life download his Chaos Music Screen-Saver for Windows 95/NT MusiNum - The Music in the Numbers MusiNum is a wonderful program provided as freeware by Lars Kindermann . At his interactive site you can try out his program and download it for use on your own computer. Most of the music on this site was composed using MusiNum. Fractal Vibes Phil Jackson offers a great selection of fractal music he created using a number of different programs. Check out his "Make-A-Midi" input form , fill it out, and Phil will create music to your specs and post it on his site. For example I composed Usrmn46c.mid with Phil's help. Visual representations of the fractals accompany many of his songs in the Galleries. Organised Chaos
    Phil Thompson's Fractal Music
    Phil calls his site "a gothic sci-fi fractal extravaganza" and he's not kidding! The site itself is a work of art.

    17. ThinkQuest : Library : Fractals And Chaos
    Main Page. About the Creators. Search Our Site. Guestbook. Citations. Topics. The Butterfly Effect. Full Blown Chaos. fractals. fractals and Chaos. Mandelbrot Set. Misc. Java Applets. Fractal music .
    http://library.thinkquest.org/26688
    Index Math Fractals
    Fractals and Chaos
    Its goal is to educate high school students (with backgrounds in algebra) about chaos theory and fractals, with a conceptual overview, historical references, and also some fractal math. Visit Site 1999 ThinkQuest Internet Challenge Languages English Students James East Brunswick High School, East Brunswick, NJ, United States Krishnan East Brunswick High School, East Brunswick, NJ, United States Seung Woo East Brunswick High School, East Brunswick, NJ, United States Coaches Tom East Brunswick Board of Education, East Brunswick, NJ, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

    18. Fractals In Music: Introductory Mathematics For Musical Analysis (Inmusic (Salt
    Buy fractals in music Introductory Mathematics for musical Analysis(Inmusic (Salt Lake City, by Charles Madden (Hardcover August
    http://www.mathbook.com/f/Fractals/Fractals_in_Music_Introductory_Mathematics_fo
    For Age: 4 years and up
    LeapPad
    by LeapFrog
    At Amazon
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    More Info

    This talking book comes with an interactive ''magic pen'' that works like a hand-held computer mouse pointer. Children can opt to turn the paper pages and listen to the story read with different voices for each character. Or they can interrupt the read-aloud session to play with the magic pen (permanently attached with a wire). They can point the pen tip to any word on a page and hear it pronounced, or touch a picture and hear a sound effect (such as ''Strike one!'' for the baseball bat). Very similar to the popular Living Books computer games, this 10-by-11-inch book is more portable than a home computer. Stories in this set include Lil's Loose Tooth, Richard Scarry's Best Word Book Ever, and Winnie the Pooh in A Sweet Good Morning. The set also includes a paper piano keyboard and map and human anatomy games. Gail Hudson
    Batteries: 4 AA batteries required.
    Sir Cumference and the Great Knight of Angleland: A Math Adventure
    by Cindy Neuschwander, Wayne Geehan (Illustrator) (Paperback - April 2001)
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    19. Fractals Store
    fractals in music Introductory Mathematics for musical Analysis (Inmusic(Salt Lake City, by Charles Madden (Hardcover August
    http://www.mathbook.com/f/Fractals/
    For Age: 4 years and up
    LeapPad
    by LeapFrog
    At Amazon
    on 4-15-2003.
    More Info

    This talking book comes with an interactive ''magic pen'' that works like a hand-held computer mouse pointer. Children can opt to turn the paper pages and listen to the story read with different voices for each character. Or they can interrupt the read-aloud session to play with the magic pen (permanently attached with a wire). They can point the pen tip to any word on a page and hear it pronounced, or touch a picture and hear a sound effect (such as ''Strike one!'' for the baseball bat). Very similar to the popular Living Books computer games, this 10-by-11-inch book is more portable than a home computer. Stories in this set include Lil's Loose Tooth, Richard Scarry's Best Word Book Ever, and Winnie the Pooh in A Sweet Good Morning. The set also includes a paper piano keyboard and map and human anatomy games. Gail Hudson
    Batteries: 4 AA batteries required.
    Sir Cumference and the Great Knight of Angleland: A Math Adventure
    by Cindy Neuschwander, Wayne Geehan (Illustrator) (Paperback - April 2001)
    Visit Our Sites: Buy Law Books Top Quality Wrist Watches

    20. Compare Prices And Read Reviews On Fractals In Music: Introductory Mathematics F
    Epinions has the best comparison shopping information on fractals inMusic Introductory Mathematics for Musical Analysis. Compare
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