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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

61. More Fractals
Fractal music Sites and Generators software links. http//users.net1inc.net/tlc/recent.htm. Inever new that fractal music exists !!!!
http://groups.msn.com/MoreFractals/fractalmusic.msnw
var nEditorialCatId = 25; MSN Home My MSN Hotmail Shopping ... Money Web Search: document.write(''); Groups Groups Home My Groups Language ... Help More Fractals MoreFractals@groups.msn.com What's New Join Now Welcome to More Fractals Site map ... Tools Fractal Music Sites and Generators software links http://users.net1inc.net/tlc/recent.htm http://thinks.com/sounds/fractal.htm http://www.fin.ne.jp/~yokubota/mandele.shtml ( mandelbrot music programm ) http://www.geocities.com/SiliconValley/Haven/4386/ (FractMus music generator ) http://www.musoft-builders.com/links/amg.shtml ( Musical Generator shareware ) Our Members compositions First of all just a little note from me . I never new that fractal music exists !!!! If you don't know about it you probably will be the same excited as me :-))) Can you imagine we can compose fractal music of our own ! The only thing we need - good music generator and I found them , tried some of them and here is my first attempts on creating music :-) Hmmmm .... I hope I can call it music :-) You probably interested to see how looks like the music that you heard on our main page . Here you go !

62. File Library At Channel 1: Fractals
491, wtf20.zip, 45799, 1118-93, The Well Tempered Fractal v2.0 - an interactivefractal music generator. Generates musical melodies by mapping fractals to music.
http://www.filelibrary.com/Contents/DOS/94/14.html
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(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

63. File Library At Channel 1: Music/Sound Programs
wtf23.zip, 58199, 1231-93, The Well Tempered Fractal 2.3e, generates musical melodiesby mapping fractals to music Has several fractal types and musical options.
http://www.filelibrary.com/Contents/DOS/38/24.html
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Jump to page number NEW this page Filename
(click to download) Size Date Description warsp251.zip Warajevo ZX Spectrum emulator v2.51 Unique program developed in Sarajevo that emulates MIDI interface on Spectrum 128 and Sinclair Net. wavcnv.zip WavConv; A DOS utility for converting 8-bit sound files among many of the most common PC formats. It will convert a file from or to any of the following: Covox Speech Thing VoiceMaster (VMFs), MS Windows 3.1 (WAV), DSound (SNDs), SoundBlaster (VOCs) and more. wave12.zip WAVE 1.2 for the Turtle Beach Monterey sound card; minor upgrade taken from the Turtle Beach Internet site. This version is compatible with TB's WavePatch sound utility. wavemake.zip Wavmaker - will generate wav files with pure sine or square wave tones. It does not require a sound card and is not a wav player. wavepool.zip

64. AudioVisualizers Library Videos: Images Of Chaos
Images of Chaos fractals to music. Images of Chaos - fractals tomusic Industrial Street Productions 1993, 53 min Box says Let
http://www.audiovisualizers.com/library/catagory/reviews/imagesof/imagesof.htm
Images of Chaos - Fractals to Music Images of Chaos - Fractals to Music
Industrial Street Productions 1993, 53 min
Box says: Let Your Television Evolve:
Futurists, artists, and cyberpunks have long prophesied of the day when television would evolve into an active platform for art. In the future, they've said, we will use television and computers to turn our homes into 21st century galleries with ever-changing new images opening our minds to alternative worlds and new vistas. The future is now. Images of Chaos is a revolutionary gallery of images for the mind. Unlike anything seen before, the images are graphic incarnations of advanced mathematic formulas. You may discover surreal worlds or strange creatures in the images, but they have all been created entirely as the result of mathematics, "sculpted" by adjusting variables and formulas based on the groundbreaking science of Chaos. Featuring an original score by innovative composer Mark Wilson, Images of Chaos is a kaleidoscopic collection of fractal images. Think of it as a 21st Century lava lamp for your television.
Order Info: Industrial Street Productions, 8424A Santa Monica Blvd, Suite # 801, West Hollywood, CA, 90069. USA. (310) 652 6997.

65. AudioVisualizers: Video Library Category Listings: Fractals
fractals Fractasia fractals to Classical music Images of Chaos - fractals to musicPsychotronic CyberSpace - fractals hallway reception tools library
http://www.audiovisualizers.com/library/catagory/category/fractals.htm
Fractals
Fractasia
- Fractals to Classical Music
Images of Chaos
- Fractals to Music
Psychotronic CyberSpace
- Fractals
hallway
reception tools library ... school

66. Computational Musicology, Fractal Music, Chaos -°è»êÀ½¾ÇÇÐ, ÇÁ·¢Å
music and interesting sounds have specific structures in the spectral domain.Many of wellknown fractals also have similar structures such as repetition
http://brainew.com/research/music/
Computational Musicology, Fractal Music, chaos -°è»êÀ½¾ÇÇÐ, ÇÁ·¢Å»À½¾Ç, ÇÁ·¢Å» À½¾Ç, Ä«¿À½ºÀ½¾Ç Home Selections Brain AI ... Personal visit count: 1854
Fractal Music on Spectrum Domain
1. Introduction
Computational Musicology
What is Computational music?
Logics and mathematics have already been a source of inspiration for composers in the music history. Computational Musicology mainly deals with the computational aspects of music as both of micro and macro level such as wave, frequency, scale, theme, harmony, counterpoint, etc. The importance of computational musicology has been increasing since the advent of the computer, a new and powerful musical instrument in music history.
Areas in computational music
  • Automatic music composition Imitation of the specific style of great musicians Human-like composition Fractal music
The pioneer of computational music
Iannis Xenakis
2. Fractal Music Method by Jung, Sung Young
Music and interesting sounds have specific structures in the spectral domain. Many of well-known fractals also have similar structures such as repetition, variation, similarity in micro and macro level. We can listen to the beauty of fractal world through sound. You can hear a rythm and melody which are hidden inside of fractal. Rythm and melody can be produced by the spectral transformation from fractal. click to listen to this fractals on sound
2.1 Fractal world on the spectrum domain

67. The Nature Of Fractal Music By Solomon
For those interested in the use of fractals to create music, a list of ofwebsites is provided at the end of this exposition. Fractal music Links.
http://music.theory.home.att.net/fracmus.htm
The Fractal Nature of Music
Please be patient as this page may take a while to load but it's worth it ! An animated Mandelbrot fractal showing a large magnification zoom. (To review this fractal animation after it is fully loaded (which may take a few minutes), back out (Alt ) and immediately return (Alt ) to this page or right-click the image and choose "View Image".) The topic of this essay is the manifestation of fractal-like structures in existing music, rather than the creation of new music. For those interested in the use of fractals to create music, a list of of websites is provided at the end of this exposition. The word "fractal" means "broken" and originally referred to fractional dimensions and irregular (hence "broken") surfaces. Fractal geometry is a new branch of experiential mathematics that recognizes that objects in the real, or natural, world are not purely square, triangular, circular, spherical, cylindrical, etc., but, rather that the latter are are only idealized geometric models. Planet Earth is described in traditional science as a sphere or ellipsoid, although its surface is not smooth, but rough, with mountains and valleys. The coastline and boundary of India may be described in Euclidean geometry as a triangle, but it is really very complex and irregular. Link: More About Fractals (Use your "Go Back" key or [Ctrl

68. [ Wu :: Fractals ]
(See the Gallery for more fractal art.). fractals can even be used to make music! Youcan listen to a fractal music sample by clicking on the link below
http://www.ocf.berkeley.edu/~wwu/fractals/fractals.html
; Registration code (if you have it) ; Optional URL link when the applet ; Reglink opened in new frame? ; Name of new frame for reglink ; Statusbar message ; Number of of iterations each branch ; Branches per iteration ; Speed of morphs through shapes ; Rotation speed within iterations ; Rotation speed of whole fractal ; Length decrease each iteration ; Length of the starting line ; Drawing pen size (1..3) ; Progressive pen increase (YES,NO) ; Inverse progressive pen (YES,NO) ; Pen progression stepping ; Half iter skipping ("YES" or "NO") ; Background image (img name or "NO") ; Background colour (red component) ; Background colour (green component) ; Background colour (blue component) ; Fractal colour 1 (red component) ; Fractal colour 1 (green component) ; Fractal colour 1 (blue component) ; Fractal colour 2 (red component) ; Fractal colour 2 (green component)

69. The Music Of José Oscar Marques
operational). The Strange Beauty of Fractal music. fractals employed. TOPOF PAGE. About fractals and Fractal music (and a few links) Fractal
http://www.unicamp.br/~jmarques/mus/fractal/
This is a mirror of the original MIDIWORLD page
(no longer operational) The Strange Beauty of Fractal Music Fractals are abstract mathematical objects which, as such, cannot be seen or heard, but their structure can be used to model computer generation of images that may be visually very attractive. Fractal images have been popular for more than a decade, but I think we are just scratching the surface of the possibilities of fractal music. The compositions on this page aim to explore some of these possibilities, showing that recursive algorithms can be employed to create music of the same strange beauty as the richly decorated fractal picture at the side . The Music General Info Links About me The Music (NEW) Check here the music in MP3 format: The CD The pieces are listed newest first. They cover a variety of styles, since "fractal music" doesn't mean a musical genre but rather a method at the composer's disposal for his or her own expressive purposes. In the end, as it happens with any other method of composition, only the musical merits of the result should actually count. Three Canons
March 1998 Old Stones October 1997 "Up the Beat", for jazz ensemble

70. UW Libraries - Music Library - Electronic And Computer Music
fractals. Fractal music; Fractal music Lab; MusiNum The music in the Numbersby Lars Kindermann; Fractal Vibes (formerly Phil s Fractal music); FractMus.
http://www.lib.washington.edu/music/electronic.html
Electronic and Computer Music
Computer and/or Electronic Music Sites
MIDI
Software
Miscellaneous
Fractals
MIDI Files

71. Generation5 - Applications In Music
Fractal music. What do fractals have to do with music? If you are interestedin finding more about fractal music, please see our links section.
http://www.gamedev.net/reference/articles/article555.asp
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Applications in Music
By James Matthews Printable Version The Artificial Intelligence applications in music are endless - unfortunately, at present there is very little so show for it. Artificial Intelligence and music are at either ends of the spectrum, AI being seen as the epitomy of computer science, and music the epitomy of art and abstractness. Dynamic and autonomous music creation has endless possibilities - pieces could be composed in seconds, for garden centre, elevator and trance music! Computers could provide brilliant 'jam' partners for guitarists, blues/jazz players to help develop their style. Computers could provide piano accompaniment for orchestral practices. The possibilities are endless ! Yet how can all of this be achieved?
Generating Computer Music
Creating music takes a certain amount of inspiration to get a piece started. How do we inspire computers? As of yet, there is no music-generating program that takes no human input. Most programs at the moment require the human user to set various parameters and options - these are used by the computer to generate the piece. A lot of music programs use genetic algorithms as a means of generating pieces. GenJam by

72. Project Summary
The second area I wanted to find out about is how to make music outof fractals, which I had read about on the internet. I did this
http://www.sciencefairs.bc.ca/regions/gvrsf/2003public/m6c.html
The Sound Of Fractals
Gregory Duggan
Collingwood School
Floor Location : M 6 C
The second area I wanted to find out about is how to make music out of fractals, which I had read about on the internet. I did this by taking data obtained from the program I developed to create the Mandelbrot fractal, and I found a method to convert the data into musical notes. This involved transforming decimal numbers first into binary numbers, and then into a musical scale. Having got this far, the tricky part was how to take all the musical notes I created and to put them into a computer program so that I could actually listen to the Mandelbrot fractal.

73. Fractals Book Store Featuring 169 Fractals And Related Books At Discount Prices.
Buy it Now! fractals in music Introductory Mathematics for musicalAnalysis by Charles Madden (Hardcover August 1999) fractals
http://rbookshop.com/computer_books/f/Fractals/
Search Now: NOTICE : All prices, availability, and specifications are subject to verification by their respective retailers.
info@rbookshop.com

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Fractals Books Buy Fractals books and other Computer Books here at discount prices! Choose from a total of 169 Fractals items sorted by poularity. Click on any Fractals book for reviews, product descriptions, prices, and buying information.
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ALPHABETICAL SALES RANK Fractals, Googols and Other Mathematical Tales by Theoni Pappas (Paperback - March 1993) List Price - $10.95 Amazon Price: on 6-6-2004 The Fractal Murders by Mark Cohen (Author) (Hardcover ) List Price - $25.00 Amazon Price: on 6-6-2004 Painter 8 Creativity: Digital Artist's Handbook by Jeremy Sutton (Author) (Paperback ) List Price - $49.99 Amazon Price: on 6-6-2004 Trading Chaos : Maximize Profits with Proven Technical...

74. Fractal Music
fractal music. Gary Lee Nelson, a professor at the Conservatory of musicin Oberlin, Ohio, explains to us what fractals are all about.
http://www.pulseplanet.com/archive/Aug01/2479.html
Program #2479
August 2001
Fractal Music
ambience:
musical composition entitled Goss
All music is said to have some basis in numbers and now a relatively new branch of mathematics has given rise to its own incarnation of music. I'm Jim Metzner, and this is the Pulse of the Planet, presented by DuPont. We're listening to the conversion of mathematical equations into what's called fractal music. Gary Lee Nelson, a professor at the Conservatory of Music in Oberlin, Ohio, explains to us what fractals are all about. "Fractals, in general involve, mathematics. Almost all fractals can finally be represented as a series of numbers. And if you were to use those numbers to produce graphic images, you would get digital paintings. If you interpret the numbers as musical elements - melody, harmony, rhythm - then the result would be called fractal music, or music derived from fractal mathematics There's a real life analogy to fractals that I think most people have experienced, or at least observed. Imagine you are sitting in a barber shop and you are looking at your image in the mirror. Of course, you see yourself, but you also see your reflection from the mirror on the opposite wall. And those reflections are moving back and forth, out to infinity. So this is a simple process, and a simple input - your image is the input - the process of the reflecting mirrors, and the complex result, is this pattern of images that goes off, shrinking in size, until they kind of disappear from sight."

75. :: Ez2Find :: Fractal Music
fractal.htm; Fractal music Lab Site Info - Translate - Open New WindowTools and information on exploring and advancing the musical use of fractals.
http://ez2find.com/cgi-bin/directory/meta/search.pl/Arts/Music/Styles/Experiment
Guide : Fractal Music Global Metasearch
Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode
All Words Any Word Phrase Results
Timeout
Depth
Adult Filter Add to Favorites Other Search Web News Newsgroups Images
Invisible Web Metasearch
Dotmusic
Astraweb Launch Video MIDI Farm ... AudioPhilez
Guides Fractal Music
ez2Find Home Directory Arts Music ... Experimental : Fractal Music Related Categories Science: Math: Chaos and Fractals
Web Sites

76. Fractals
Enter the wonderful world of fractals where mathematics meets art and music.
http://thinks.com/fractals.htm
Home
Fractal Pages at Thinks.com
Enter the wonderful world of fractals - where mathematics meets art and music.
Sprott's Fractal of the Day

Fractal Software

Fractals WebGuide

Fractal Music WebGuide
...
Books about Fractals and Fractal Art

Search WWW Search Thinks.com
Search for in Baby Books Classical Music DVD Electronics Magazines Outdoor Living Popular Music Software Video About Thinks.com
Our other sites: AtoZee (Collectibles), Thinks Global (Travel), 21st Century Home (US) 21st Century Home (UK)
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77. Chaffey's Fractal Links On The Web
Chaffey High School's fractals on the Web. http//www.chaffey.org/fractals/ Last Updated February 28, 2003. This site should be renovated soon, please excuse the webmaster's lack of construction.
http://www.chaffey.org/fractals
Chaffey High School's FRACTALS on the Web
http://www.chaffey.org/fractals/ Last Updated February 28, 2003
This site should be renovated soon, please excuse the webmaster's lack of construction. Welcome to the original Chaffey High School's Fractal Links of the Web. These pages where started as a hobby/extra curricular activity back in 1993, and have grown to be a pretty large website for alumni of Chaffey High School, as well as general links resource for schools. Fractals are very interesting and mathematical occurrences. Chances are, if you have opened your eyes, you've seen Fractals. This site, Chaffey's Fractal Links, is meant as a resource for everybody to use as a tool in search of fractal information, programs, articles and other fractal related pages on the Internet. This page has been up since 1993 and is continuing to grow in content. More will be coming soon... CHS Home Fractals Home About Fractals Awards ... Theory

78. Chaos Theory And Fractals
History of chaos as well as extensive information on Chaos Theory and fractals. Contains several pictures of fractals and links to other Chaos Theory and fractals pages.
http://www.mathjmendl.org/chaos/
Chaos Theory and Fractals
By Jonathan Mendelson and Elana Blumenthal
Outline
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
Sir Isaac Newton 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

79. Efg's Fractals And Chaos Page
Several Fractal and Chaos projects, including Evolution of Mandelbrot Set, Fractal Discovery Lab, IFS images, Lorenz and other Strange Attractors.
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

80. Cynthia Lanius' Lessons: A Fractals Lesson - Introduction
Features class exercises and lessons or making fractals. Includes explanation of this unique image and types of formulas that are used to create it.
http://math.rice.edu/~lanius/frac/
Cynthia Lanius
Fractals
Pictured: A Famous Fractal - The Mandelbrot Set
A Fractals Unit for Elementary and Middle School Students
That Adults are Free to Enjoy
Table of Contents
Introduction Why study fractals?
What's so hot about

fractals, anyway?
Making fractals
Sierpinski Triangle

Using Java

Math questions

Sierpinski Meets Pascal
...
Using Java
Fractal Properties
Self-similarity

Fractional dimension
Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Comments My fractals mail Send fractals mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received
What are Fractals?
They're everywhere, those bright, weird, beautiful shapes called fractals. But what are they, really? Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. There's lots of information on the Web about fractals, but most of it is either just pretty pictures or very high-level mathematics. So this fractals site is for kids, to help them understand what the weird pictures are all about - that it's math - and that it's fun! Teachers: Every lesson has a print version for classroom use.

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