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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

161. Epsilon: Ambient Music, Beginnings And Implications, By Chris Melchior
Ambient music may be defined as music in which in which fractal qualities Ambient music, consisting of predominantly fractal rather than linear patterns
http://music.hyperreal.org/epsilon/info/melchior.html
AMBIENT MUSIC, BEGINNINGS AND IMPLICATIONS.
by Chris Melchior
INTRODUCTION
Ambient music has arisen recently out of many diverse roots in music and the arts, and has implications that are varied and interesting because they overlap with so many fascinating concepts in art, science and philosophy.
DEFINITIONS OF CONCEPTS: Music, fractals, ambient
From Webster's 3rd New International Dictionary of the English Language, unabridged, the definition of music is "the science or art of incorporating pleasing, expressive or intelligible combinations of vocal and instrumental tones into a composition having definite structure and continuity," or alternatively :- "Vocal or instrumental sounds having rhythm, melody or harmony." i.e. music is defined as only consisting of vocal or instrumental sounds, and it is implied that it has linear rather than fractal structural qualities (see the definition of fractals, below). Given this definition of music, is John Cage's 4 minutes 33 (see below) music, as it doesn't necessarily have any vocal or instrumental sounds, or linear structural qualities? The definition of 'ambient' from Webster's is :- "to go around, surround, encompass. An encompassing environment, or atmosphere" [1]. If one combines the above definitions from Webster's [1], ambient music would be vocal or instrumental tones having linear structural qualities, and creating an encompassing environment. This is clearly not a good definition of ambient music, as ambient music does not necessarily have any linear structural qualities or instrumental or vocal tones. So, attemting to reach a definition of ambient music by combining the definitions from Webster's [1] of music and ambient, is not proving to be successful.

162. Chaos, Fractals, And Arcadia
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
http://math.bu.edu/DYSYS/arcadia/
Chaos, Fractals, and Arcadia
Robert L. Devaney
Department of Mathematics
Boston University
Boston, MA 02215
Below you will find an animated description of some of the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia . For access to some of the mathematical software that generates some of the images contained herein, visit the Dynamical Systems and Technology Project at Boston University. To purchase a video involving some of the mathematical ideas in Arcadia, together with a taped discussion by Tom Stoppard, visit the Mathematical Sciences Research Institute at the University of California, Berkeley.
Some pictures from Arcadia We welcome your feedback on this material. Please send any comments or suggestions to Robert L. Devaney at bob@bu.edu Introduction (Next Section)
(Return to Dynamical Systems and Technology Home Page

163. Wallpaper From Mysticbrews And GLNML Hosting
Wallpaper in 800 x 600 and 1024x768 sizes that cover holidays, miscellaneous, shapes and fractals, and winter.
http://mysticbrews.com/wallpapers/wallpapersglnml.shtml
Wallpaper from Mysticbrews and GLNML Hosting
Click on the thumbnail, and than right click on the pictures, and "Save As Wallpaper" (or "Set As Wallpaper"). Hope you enjoy these, and do stop back again, we're always adding more.
If you see only 1 wallpaper, than the thumbnail will take you to the 800x600 size, the text link 1024x768 will take you to, well :) of course, to the 1024x768.
DESKTOP WALLPAPER INDEX
SHAPES - FRACTUALS
SHAPES 2
S and M
(that's Sunshine and Moonshine :)
WINTER
Flowers, Trees, and Nature
MISCELLANEOUS
HOLIDAY WALLPAPER ... Design Work

164. Tamurilart.com: Tamuril's Digital Art Exhibit
Featuring 3D works, fractals, and vector illustrations. Images can be downloaded or viewed at high resolution.
http://www.tamurilart.com/
Main
Site Information

Memberships

Child-Safe Ratings
...
Privacy Policy

New Silver Winner
Lincoln Scout Band won my Award!
New Bronze Winner
Tonkinart won my Award!
New Artwork Added
Morning added to 3d gallery in the Art Exhibit. Hello visitor, and welcome to Tamuril's (Previously Retro-Teknix's) new website! I hope you enjoy the new interface, as I feel it will allow more room for my variety in content and range of styles. Within this site there are many features to explore: You will find my original digital paintings, desktop wallpapers, free graphics and templates, my awards program, and other quality digital information. You may surf through my site using main links at the top and sub links to the left. If you get confused, just click 'Site Map' for an overview. My site is frequently updated, so don't forget to check back for new artwork and freebies. I hope you enjoy my site and come again soon! Psalm 62:7- In God is my salvation and my glory; The rock of my strength and my refuge, is in God. Vector Misc Web Site Templates

165. References
on the use of computer graphics, fractals, and musical techniques to find patternsin DNA and amino acid sequences. C. Pickover, Fractal Horizons The
http://fractals.iut.u-bordeaux1.fr/sci-faq/books.html
Subject: References
: What are some general references on fractals, chaos, and complexity? : Some references are: M. Barnsley, Fractals Everywhere , Academic Press Inc., 1988, 1993. ISBN 0-12-079062-9. This is an excellent text book on fractals. This is probably the best book for learning about the math underpinning fractals. It is also a good source for new fractal types. M. Barnsley, The Desktop Fractal Design System Versions 1 and 2. 1992, 1988. Academic Press. Available from Iterated Systems. M. Barnsley and P H Lyman, Fractal Image Compression . 1993. AK Peters Limited. Available from Iterated Systems. M. Barnsley and L. Anson, The Fractal Transform , Jones and Bartlett, April, 1993. ISBN 0-86720-218-1. This book is a sequel to Fractals Everywhere . Without assuming a great deal of technical knowledge, the authors explain the workings of the Fractal Transform (tm) . The Fractal Transform is the compression tool for storing high-quality images in a minimal amount of space on a computer. Barnsley uses examples and algorithms to explain how to transform a stored pixel image into its fractal representation. R. Devaney and L. Keen, eds.

166. Doorschakeling
Rekenen en schatten, verbanden, grafieken, functies, vergelijkingen, analyse, grafen en matrices, statistiek en kansberekening, meetkunde en wiskundige kunst. Informatie over rekenmachines, je kunt 'fractals' bekijken en je kunt spelletjes doen.
http://www.digischool.nl/wi/

167. Fractal - Wikipedia, The Free Encyclopedia
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two and three dimensional illustration sets.
http://en.wikipedia.org/wiki/Fractals
Fractal
From Wikipedia, the free encyclopedia.
(Redirected from Fractals The Mandelbrot set , named after its discoverer, is a famous example of a fractal. The Mandelbrot set , named after its discoverer, is a famous example of a fractal. A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be 'broken up' in a radical way. Some of the best examples can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and they may actually have a self-similar structure that occurs at different levels of magnification. In many cases, a fractal can be generated by a repeating pattern, in a typically recursive or iterative process. The term fractal was coined in by Beno®t Mandelbrot , from the Latin fractus or "broken". Before Mandelbrot coined his term, the common name for such structures (the Koch snowflake , for example) was monster curve Fractals of many kinds were originally studied as mathematical objects. Fractal geometry is the branch of mathematics which studies the properties and behaviour of fractals. It describes many situations which cannot be explained easily by classical geometry, and has often been applied in

168. Fractal Wallpaper Manager - Redecorator - It Will Change Your Wallpaper
Redecorator can change your desktop wallpaper as often as you like, as well as create beautiful fractals.
http://www.seraline.com/wallpaper/
Redecorator Fractal Wallpaper Manager
It will change your wallpaper
Fractal Wallpaper Purchase
Download

Support

Screensavers
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Email us
R edecorator is a wallpaper manager, or randomizer, and image creator for Windows 95/98/ME/XP/2000. R edecorator will create a wide variety of beautiful fractals for your backgrounds. I t also allows you to have your desktop background images come from any folder on your computer, and your background can change automatically as often as you like. R edecorator can also optionally create seamless tiles of your images to give the appearance of a single large texture. R edecorator can color your icon text so that it remains readable, along with transparent icon backgrounds so that more of your wallpaper shows through. O ptionally displays the current date R edecorator is "try before you buy" software, US$9.95, with a 14 day evaluation period. T o download a Free 14 day Trial Version with automatic installation (640K), click here
  • If your browser gives you the option to Open or Save the file, you can choose Open . This will automatically start the installation process at the end of the download.
    If you choose to Save the file, then after downloading, locate RedecoratorTrial.exe in your download folder using Windows Explorer, and double-click on it to start the installation.

169. Index
A Site of art images, fractals, digital art, abatract art, hand blown glass and photography as an art form
http://jcmacpherson.com
A Small Artist Colony
Finally updated in June 2005 after two years of being lazy ;-)
Hi, you have arrived at
John Charles Macpherson's site
You can e-mail me at
jc@jcmacpherson.com

Me at work. If you enjoy this website, please visit my other one. Las Vegas Fine Art So, what is art? Art is something made by an artist.
What is good art? Good art is stuff you like.
Bad art is stuff you do not like. There, you now have the equivalent
of an MFA which normally takes 6 years of advanced study.
So, how can you recognize an artist? An artist has three main characteristics: first, visionan artist sees things differently. second, abilityto communicate what he or she sees. third, artistic temperamentall artists, good or bad, think that their stuff is the absolute greatest. (or else why bother?)
So, what is on this site? First, and most importantly, galleries of my new art form for the 21st century. Here you will find hand blown glass from my previous life. Here, Joy, my bride, sells her own handmade baby quilts at bargain prices. Note: No gemstones until after Sept. 15, '05

170. Computer Music (G6610, Fall 2003) Week3
Gary Nelson s web page the king of fractal music; basic fractal music bibliography the fractal music project this has one of the most annoying
http://music.columbia.edu/cmc/courses/g6610/fall2003/week3/
Links
Code
  • G6610 older class this has a good disussion (with purty pictures even!) of the "fractal reflection" exercise we did in class. Again, some of the links are a little old... the link to the RTcmix STEREO instrument documentation is older, and use the xmountains.tar.gz package linked below here for Mac OSX.
  • reflect.tar.gz the code for our 'fractal reflection' exercise (described in the "G6610 older class" link above)
  • mandel.tar.gz

171. Fractals And Multi Layer Coloring Algorithms
Scientific paper of the University of the Basque Country, Spain, addressing the mathematical aspects of multi layer colorization. Includes examples and references.
http://www.mi.sanu.ac.yu/vismath/javier1
Fractals and multi layer
coloring algorithms
Javier Barrallo and Santiago Sanchez Mathematics, Physics and Computer Science The University of the Basque Country School of Architecture. Plaza Onati, 2. E-mail: mapbacaj@sa.ehu.es Abstract
The focus of exploration in new fractal techniques is shifting away from fractal formulas and towards coloring algorithms. This paper provides an overview of the coloring algorithms in popular use and how they can be combined and superposed. We call these multi layer fractals, and they are the source of some of the richest fractal imagery being produced today. In this way, even a limited collection of fractal coloring algorithms can be combined in almost endless ways. 1. Dynamical systems and fractals Dynamical systems are a well-known branch of mathematics, but until the arrival of computers the sheer number of calculations involved made them impractical for real use. The computer’s ability to perform rapid calculations allows us to condense billions of calculations into results we can digest. Benoit Mandelbrot was the first one to use computers to produce graphical representations of dynamical systems in the complex plane, based on the quadratic formulas described by the French mathematician Gaston Julia at the beginning of the 20th century. During the 1980s, fractal enthusiasts began exploring fractals for their artistic merit, not for their mathematical significance. While mathematics was the tool, the focus was art. As the fractal equation itself was the most obvious mathematical element, fractal artists experimented with new equations, introducing hundreds of different fractal types. By carefully choosing parameters to refine form, color, and location, these explorers introduced the concept of fractal art.

172. Index Of Free Desktop Wallpapers / Backgrounds
3D rendered images and fractals for use as free desktop wallpapers. All graphics are in JPG format.
http://www.shineout.com/display/desktop_wallpapers.htm
Free computer generated desktop wallpapers. For better looking desktop. Graphics are in jpg format DESKTOP WALLPAPERS LINKS WORTH VISITING
Click on a Page Number

173. Fractal Midi Music Spanky.triumf.ca.mid
as well as to the sophistication on the fractal music generation software.Fractal music generation can be as simple as a single audio tone,
http://spanky.triumf.ca/www/fractal-info/f-music.htm
Fractal Music
Fractals don't necessarily have to be represented graphically. Due to their self similar nature and infinite variation, many fractals lend themselves to being interpreted as a form of music. The quality of sound produced will depend to a large extent on the quality of the sound system available with the computer used, as well as to the sophistication on the fractal music generation software. Fractal music generation can be as simple as a single audio tone, varying in pitch in a seemingly random fashion, or it can be multiple musical instrument voices, varying in pitch and volume in a complex melodic and rhythmic pattern. Fractal music has undergone a lot of change in it's brief history. The quality will vary from noise ,to electronic windchimes, to a complex well developed musical theme. There are several good web sites dedicated to the creation of Fractal Music. Lars Kindermann's Musinum site is one of the best. It can create fractal music in real time as well as having a large collection of some of the best efforts in this realm in both midi and MP3 format. It also has links to other fractal music resources such as software for the creation of fractal music and other fractal music sites.

174. Stephen Warren's Home Page
Photo gallery, video gallery, personal information, IFS fractals and virtual business cards.
http://www.wwwdotorg.org/

Photo Gallery

Virtual Cards

Fractals

Video Gallery
...
News

Anyone can be taught to sculpt:
Michelangelo would have to be taught not to.
So it is with great programmers.
ACM SigPlan 1982, Epigrams in Programming Intelligence is not the ability to learn, but the desire.
Stephen Warren This Web page is maintained by Stephen Warren, swarren@wwwdotorg.org

175. My Site
Gallery and program with source. Includes animated threedimensional sets and attractors.
http://www.geocities.com/mischa_griesman/index.html
Visit this site - very good Flash(not my) My gallery at webshots I find some interesting effect when playing with attractors, like Chaoscope. Now I try to write program under Linux (Gnome + Gtk 2 + C). I'm not a professional programmer, so if anybody can finish this program... I SHOULD BE REALLY HAPPY. Program is Free with source code included. Enjoy! 17.Sep.2005 Download Here is a new program source Here is a new binary with gradients P.S my email updated bred24 (remove this part) @rambler.ru Old part of site: This little program make Targa height_field for Pov Ray(see images above) Of course you can use this targa file with another render. Simple user-friendly interface should not cause difficulties Let op: camera must be orthographic. Download program with source here is Pov Ray sample: scale rotate author - mongrel_watch-dog

176. Fractal Art By Vicky - Fractal Wallpaper Art Gallery For Desktop
Fractal Art Free Desktop Wallpaper Classical music, 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
http://www.abm-enterprises.net/wallpaper.html
Fractal Art
Free Desktop Wallpaper
Classical Music
FRACTALS BY VICKY
Welcome to my gallery! These images are based on a kind of math called fractal geometry, and are created by repeating simple patterns billions and trillions of times. Until today's fast computers became widely available, only mathematicians had seen them; now everyone can enjoy their intricacy and beauty. (For more explanation read Fractal Geometry
To set any of these as your desktop wallpaper on a PC, click on the thumbnail to see the full-sized picture, then right-click on the picture and select Set as Background. Mac users can save images in their Macintosh HD> Library> Desktop Pictures folder.
Buy prints and posters from art.com!

Click here or on one of the ads above.

Dandelion Tell a Friend
Gossamer
Shoulderblades
Source
Medallion Golden Dragon Bright Lights Poseidon's Throne more... Sorry, your browser doesn't support Java ; Msg in no java browsers Alphabetical index of fractals Email d.write(""); TopDepo.com

177. Railz Free 3D Wallpaper And Screensavers.
Creative 3D desktop wallpaper in three categories of landscapes, 3D art and fractals, also a user gallery. Wallpaper available in five popular sizes.
http://www.railz.net/
Welcome friends to Railz.net. This site is intended for you to view and download as wallpaper. All images on this site are © 2000-2004 by Railz.net 16062 Shay lane. Nevada City CA 95959 USA Site first uploaded: 18-July-2000 privacy policy

178. Computational Musicology, Fractal Music, Chaos -°è»êÀ½¾ÇÇÐ, ÇÁ·¢Å
Translate this page Works of Fractal music by Jung, Sung Young Fractal music 15. composed in 2002.8 Fractal music Method by Jung, Sung Young. music and interesting sounds
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: 7308
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

179. Welcome To The Fractal Foundation
Inspiring and educating people about fractals, Chaos Theory and the interconnectedness of complex systems.
http://www.fractalfoundation.org
...is to educate and inspire people about mathematics, art, science, chaos theory and nature. We focus particularly on efforts to reach young people with our educational programs , and we also connect with adults through our scholarship and art sponsorship programs.
We believe that understanding the Principles of Chaos Theory - which are so beautifully illustrated by fractals - is essential to harmonious and sustainable living. No longer is it safe to assume that the cultural, economic and ecological systems in which we live are discrete, linear, disconnected. Rather, we must begin teaching ourselves and our children that the World is a non-linear, unpredictable, interconnected complex system. This radical new paradigm, only recently realized in the new science of Chaos Theory, is still virtually absent from conventional education. The Fractal Foundation seeks to bring these new ways of thinking into the mainstream.
The Fractal Foundation educates people about Chaos Theory and Fractals and encourages participation in art, mathematics, and computer technology by:
  • Providing educational materials, presentations and software to school children (K-12), teaching them to explore fractals themselves.

180. Realtime Mandelbrot Fractal Generation CGI
Applet to explore the Mandelbrot set in real time.
http://mandelbrot.collettivamente.com
Mandelbrot Fractals Generator
This site is a program that allows everyone to explore the fashinating word of Fractals. Fractal is a term coined by Benoit Mandelbrot to refer to a structure bearing statistically similar details over a wide range of scales. Click on the image to zoom, on borders to pan
Restart

Image size:
infx: -2 supx: 1 infy: -1.5 supy: 1.5
colormap: volcano.map

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