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Fractals & Music: more detail

Fractal Music, Hypercards and More Mathematical Recreations from "Scientific American" by Martin Gardner, 1991-11-30
Fractals in Music: Introductory Mathematics for Musical Analysis Second Edition (Inmusic) by Charles Madden, 2007-04-23
Music and Mathematics: From Pythagoras to Fractals
Fractal Music, Hypercards and More. Mathematical Recreations from Scientific Ame by Martin Gardner, 1992-01-01
Fractal Music, Hypercards and More : Mathematical Recreations from Scientific Am by Martin Gardner, 1991-01-01
Fractal Fantasy, the Art of Mathematics by Charles Fitch, Music by Michael Angelo Strasmich, 1987
Music And Mathematics: From Pythagoras To Fractals by Raymond Flood, Robin Wilson, Robin J. Wilson John Fauvel, 2003
Formalised composition on the spectral and fractal trails (Skrifter fran Musikvetenskapliga institutionen, Goteborgs Universitet) by Magnus Eldenius, 1998

lists with details

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/

Extractions: 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)
Fractal Music
Q14 What is some information on fractal music? 2. C. Dodge, A musicalFractal, _Computer music Journal_ 12, 13 (Fall 1988), p. 10.
http://www.faqs.org/faqs/fractal-faq/section-14.html

Extractions: Usenet FAQs Search Web FAQs ... RFC Index ftp://spanky.triumf.ca in [pub.fractals.programs.ibmpc] WTF23.ZIP. [142.90.112.1] A fractal music C++ package is available at http://neural.hampshire.edu:10001/~gzenie/inSanity.html . Also, it may b helpful to access: http://www-ks.rus.uni-stuttgart.de/people/schulz/fmusic The Fractal Music Project (Claus-Dieter Schulz) http://www.ccsr.uiuc.edu/People/gmk/Projects/ChuaSoundMusic/ChuaSoundMusic.html Chua's Oscillator: Applications of Chaos to Sound and Music
Softology - Visions Of Chaos
Home page of a versatile Windows software by Jason Rampe. The program covers Cellular Automata, Chaos, and fractals.
http://www.softology.com.au/voc.htm

Extractions: Main Gallery Software Links ... Contact Visions Of Chaos Overview Display Features Visions Of Chaos supports displaying of fractals in 2D and 3D using OpenGL. Create AVI Movies Most of the modes in Visions Of Chaos support output to BMP frame files which can then be converted to an AVI movie. The series of frames allows easy importing into any video editing software. Visions Of Chaos supports script files to fully customize AVI creation. Numerous scripts are included to get a feel for how the AVI generation works and what it can do. AVI movies can be 2D or 3D fractals. Other movie options supported include creating a complete color cycle of a fractal, 3D rotations, stereoscopic rotations, flying over a fractal in 3D and more. Printing Features Visions Of Chaos supports printing for many of the fractal types. Seeing as printers have a much higher resolution than any screen can give, you will see much more of the fine detail in images created. The Mandelbrot Poster feature allows you to print one fractal image across multiple pages, which can then be glued together to create huge wall sized fractal images. Chaos/Fractal Music Creation Cellular Automata music, Genetic Music, L-Systems music, and music based on mathematical sequences.
3D Mountains
Shows how to create fractal mountains, 3D Mandelbrot and Julia sets, convex, stellated and polyhedra. Uses tiny Java1.1 applets and VRML worlds.
http://www.ibiblio.org/e-notes/3Dapp/Mount.htm
GENETIC SPECTRUM MODELING PROGRAM
Fractal music generation program for download and evaluation by Ray Jurgens. Samplemusic, score and online manual. ELECTRONIC ARTS RESEARCH. By. RAY JURGENS.
http://autoinfo.smartlink.net/ray/

Extractions: ELECTRONIC ARTS RESEARCH By RAY JURGENS Montrose, California USA Nothing but Fractal Space Ray Jurgens GSMP Fractal Note Generation GENETIC SPECTRUM MODELING PROGRAM (GSMP) FRACTAL MELODY GENERATOR V1.02 GSMP is a program that creates fractal music according to specific selections made by the user. It uses a genetic algorithm to mutate the randomly drawn notes into a fractal structure having periodic properties that you can specify. You can also specify the scale and initial bounds for the notes. Click on the SAMPLE SCORE below to see a test sequence. Of course, you still have to orchestrate this into something musical, and therein lies the challenge. SAMPLE SCORE To discover how this program works and some information about the interesting history of fractals in music, click on the On-Line Manual which gives a peek into this world of mathematics and music. ON-LINE MANUAL If you would like to give this a try, then down load the program. This program takes very minimal computer resources, it will even run on an old XT but very slowly. It does do a lot of computation especially if you do millions of generations.
Gromada.com - Multimedia Software
Automatically replaces your Windows 95/98 startup and shut down logos each time you restart your system. Includes a collection of pictures, including fractals and 3D images or you can add your own images.
http://www.gromada.com/1stImpression_dl.html
Index
A Site of art images, fractals, digital art, abatract art, hand blown glass and photography as an art form
http://jcmacpherson.com
Newton Basins
Introduction to basins of attraction for Newton's method and the fractals they form.
http://aleph0.clarku.edu/~djoyce/newton/newton.html

Extractions: Newton's method for finding solutions to equations leads to some fantastic images when it's applied to complex functions. You start with an initial guess for the solution which may be any number, and the method gives you a closer estimate to the solution. The next estimate will be even closer. Anyway, that's what often happens. Typically, there's more than one solution to the equation. If you start near one solution, you'll quickly get to it. But what happens if you start somewhere between two solutions? That's when you get interesting pictures. Color the complex plane according to where an initial guess will eventually take you. Give each solution a different color so that all the initial guesses that eventually eventually lead you to one to that solution are colored the same. A Newton basin is just the set of initial guesses that lead to one solution.
IBM Canada Scitechmatics
They will learn about fractal music, Internet radio, and other ways that the computercan be used to make music. This generates a piece of fractal music.
http://www.can.ibm.com/k12/scitechmatics/comp_music.html

Extractions: This lesson introduces students to computers and music. They will learn about fractal music, Internet radio, and other ways that the computer can be used to make music. The goal of this lesson is to show students that information technology is an exciting field that encompasses all subject areas, including the arts. Students should develop an appreciation for computers and music through individual and large-group activities. Objectives Fractal music is becoming one of the most exciting fields of new music research. Before introducing fractal music to the students, introduce the concept of a fractal. A fractal is an image that has been repeated over and over again. Show examples of various fractal pictures to the students and tell them, "You're probably wondering what these brightly-coloured pictures have to do with computers and music! You will soon see that the computer is going to convert these pictures into beautiful music. Let's listen."
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
Fractal Music
Buddha Gallery 1. Chaos Theory. Fractal Movies. Fractal music. Fractal Links.Fractal generated music using the Butterfly Curve and a MIDI keyboard.
http://www.imaging.robarts.ca/~lgardi/html/fractal_music.html
Dynamical Systems And Technology Project
An educational site on chaos and fractals.
http://math.bu.edu/DYSYS/dysys.html

Extractions: Boston University Zooming Sierpinski This project is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. It is directed by Robert L. Devaney of the Department of Mathematics at Boston University. At this point, there are a number of Java applets available at this site for use in teaching ideas concerning chaos and fractals. There are also several interactive papers designed to help teachers and students understand the mathematics behind such topics as iterated function systems (the chaos game) and the Mandelbrot and Julia sets. If you wish to have information about the dynamical systems group at Boston University, you are in the wrong place. Click here to go there. This is an interactive site designed to teach the mathematics behind the Mandelbrot and Julia sets. It consists of a series of tours in which you will discover some of the incredibly interesting and beautiful mathematics behind these images. The site is designed to be used by readers of
Chaos Report - Heather Elko
Brownian noise is to correlated. And interestingly, when most fractalsare converted to music, they are found to create 1/f noise.
http://pear.math.pitt.edu/mathzilla/Examples/chaos/studentReports/HeatherElko.ht

Extractions: Full Report (MS Word document) 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.
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 To The Fractal Foundation
Inspiring and educating people about fractals, Chaos Theory and the interconnectedness of complex systems.
http://www.fractalfoundation.org

Extractions: 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.
Fractal Explorer: Mandelbrot And Julia Sets (by Fabio Cesari)
A fractal tutorial for beginners. Covers Mandelbrot and Julia sets, as well as 4D fractals. Also features an interactive fractal generator.
http://www.geocities.com/fabioc

Extractions: You can always access this no-frames version of this site. If you have troubles accessing it, please let me know Many people have probably been fascinated by the infinite complexity and beauty of fractals. I wrote this brief tutorial to explain, in simple terms, how the Mandelbrot set and Julia sets are generated. This document provides an informal introduction to these subjects, and is only intended to be a starting point to learn more about fractals and fractal geometry.
Fractogroovalicious ITunes Plugin
iTunes plugin generating Julia fractals.
http://www.2tothex.com/fractogroovalicious.html
AAahAAA: The Band That Never Was - Jonas' Music?
I ve played around a little bit with some fractal based music creating apps,and for some reason decided that I should create a musical piece using the
http://www.truls.org/jonas/musik/Index_english.html

Extractions: No natural additives This stuff is what I've been doing for fun. I'm not really a musician at all, and everything is done purely on a computer, including the vocals wich are done with a singing speech syntheseizer. If you think the name is unclear, there's almost an explanation At the bottom of the page you'll also find my little shell for calling Lame from inside Cakewalk. All the music is in MP3 format. If you can't play the files, some useful software should be findable on mp3.com . If, for some strange reason, you MP3 player can't handle variable rate files everything is available in constant 128kbit/s (resulting in lower quality) as well. If you like something here that's great, otherwise it was still fun playing around with it so it doesn't really matter that much to me. Original Algorithmic Political Other Let's start with what I've actually composed myself. What?: I made this just because I made it. Or something like that. It kind of jumped out. Music A monotonous piece with lots of bass.
Cynthia Lanius' Fractals Unit: Fractal Dimension
An easy to comprehend mathematical approach to understanding the significance of the applied study of fractals.
http://math.rice.edu/~lanius/fractals/dim.html

Extractions: This Site has received A point has no dimensions - no length, no width, no height. That dot is obviously way too big to really represent a point. But we'll live with it, if we all just agree what a point really is. A line has one dimension - length. It has no width and no height, but infinite length.
Fractal Midi Music Spanky.triumf.ca.mid
Fractal music. Due to their self similar nature and infinite variation, manyfractals lend themselves to being interpreted as a form of music.
http://spanky.triumf.ca/www/fractal-info/f-music.htm

Extractions: 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.

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