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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

Ian Anderson Design - Free Screensavers And Wallpaper
Imaginative and innovative desktop wallpaper in categories of 3D art, landscapes, fractals, creatures, military, available in five popular sizes.
http://www.ianadesign.com/
Fractals Links: Mandelbrot, Pictures
Tempered Fractal v3.0 A Composer s Tool for the Derivation of Musical Motifs, Phrasesand Rhythms From The Beauty and Symmetry of fractals, Chaotic Attractors
http://kosmoi.com/Science/Mathematics/Fractals/links.shtml

Extractions: EncycloZine Astronomy Biology Chemistry ... Fractals, Googols and Other Mathematical Tales Theoni Pappas The Fractal Murders Mark Cohen Trading Chaos : Maximize Profits with Proven Technical Techniques Justine Gregory-Williams, Bill M. Williams, Marketplace Books Indra's Pearls: The Vision of Felix Klein David Mumford, Caroline Series, David Wright The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation Gary William Flake Trading Chaos : Applying Expert Techniques to Maximize Your Profits Bill M. Williams, Marketplace Books The Fractal Geometry of Nature Benoit B. Mandelbrot Fractal Geometry : Mathematical Foundations and Applications Kenneth Falconer Fractals John Briggs Heaven's Fractal Net: Retrieving Lost Visions in the Humanities William J. Jackson About Us A - Z Site Map Top Pages ... Cell Phones See also: Mathematics Fractals Kosmoi.com Science ... Fractaline is a program (a Java applet) for defining and drawing fractals. Examples for fractals you can draw with Fractaline include the Koch Curve, the Sierpinski Triangle, the Fractal Tree and the Fern. These classical fractals are only some of the endless number of possible fractals you can construct. You can start experimenting with Fractaline by modifying the predefined fractals and later create your own individual fractals from scratch. Fractaline is easy to use and lets you immediately see the results of your experiments in all their fractal beauty.
Gallery Of Symmetric Chaos Page
Includes Symmetric icons and fractals; Quilts and planar repeating patterns; Colored wallpaper patterns.
http://nothung.math.uh.edu/~mike/ag/art.html

Extractions: Images of Chaos and Symmetry This collection of images is divided into the following groups: The repeating patterns directory contains the directories Hexagonal Quilts and Square Quilts . In turn, both the Hexagonal and Square quilts directories contain subdirectories of two color hexagonal quilts and two color square quilts . These subdirectories contain `two-color' designs. A few of the images are `cycling GIF files' (for example, in the Icons directory Nite Vision appears as a a cycling GIF file). The cycling gifs are usually identified with the phrase `Image with detail'. Almost all of the designs are fairly new. Versions of one or two of the designs have appeared previously in the book Symmetry in Chaos by Michael Field and Martin Golubitsky (OUP, 1992) - I have indicated those specifically. Several of the images shown on these pages have appeared in exhibitions (Including: The Frontier between art and Science , International Exhibition [Valladolid, March 1-15, Salamanca, April 6-23, Leon, April 26-May 14, Granada (June/July), Buenos Aires, Belgrade, Vienna, late 2000];
Aliceia
Collection of digital paintings and abstractions, and fractals. Also includes colored pencil drawings.
http://www.aliceia.de/
Music Of The Heart
scaling pattern. Dr. Voss and others have also used computergeneratedfractals to create musical sequences. These recordings are
http://polymer.bu.edu/music/

Extractions: The MIDI music files found on this page can be best heard with the Beatnik plug-in The Music of the Heart is derived from electrocardiogram (ECG) data, actual digital recordings of the electrical signals of the human heart. These HeartSongs began as musical notes mapped from the heartbeat data. The composer then added harmonies and rhythm to make pleasant sounding music. Listen to these HeartSongs MIDI files by clicking on the controls. Can you tell which 3 compositions are based on "healthy" heart data? (Hint: read below) "HeartSong One" "HeartSong Two" "HeartSong Three" "HeartSong Four" "HeartSong Five" "HeartSong Six" There is also a hands-on exhibit at the Boston Museum of Science which allows museum-goers to record their own electrocardiogram and, in real time, listen to the music it produces. This 'heart music' created by museum-goers is different from the HeartSongs above which were 'interpreted' by a composer (i.e., chords and rhythm were added by the composer on top of the melody created from the data). Heart music you would hear at the museum exhibit which is based solely on the raw data sounds something like this: "Sample 'Real-Time' Heart Music" How can your heart make music?
Fractal Art Screen Savers
Original fractal art screen savers and custom made. Windows 95/98/ME/NT/2000
http://fractalarts.com/SFDA/screensavers.html

Extractions: Home What Are Fractals? Screensavers Art Prints Purchase Screensavers Special Offers Support Testimonials Contact Links Free Screen Saver Downloads Thank you for your interest in Seattle Fractals Digital Art screensavers. If you have already evaluated one of the screensavers and are ready to purchase one, please select "Purchase Screensavers" from the link menu or click this link: Buy Now These screensavers are available as a free download and are fully functional for a 10 day trial evaluation. You get to try before you buy with no obligation! These screensavers are for use on Windows 95/98/ME/NT/2000/XP computers. They have over 20 transition effects, Microsoft Plus! features, Screensaver Control tray utility, Desktop Quickstart, full install/uninstall feature and more. Ver. 2.0 releases I have released updated versions of my first five screensavers. These have additional content, and many new features. If you have previously purchased these screensavers the upgrade is free! Simply uninstall the previous version, download and install the updated version and re-enter your registration information. Limited Edition Collectors CD Fractalarts 2003 CD I am offering a limited edition (350 copies) screensaver CD compilation that is a collection of favorites from previous screensavers as well as new work previously unpublished. This version has many new features unavailable in my downloadable screensavers. Your CD will be numbered and signed by the artist. Click
The Computational Beauty Of Nature
Companion site for the book by Gary William Flake. Contains applets and source code for simulations of fractals, chaos, complex systems, and adaptation.
http://mitpress.mit.edu/books/FLAOH/cbnhtml/
The Math Forum - Math Library - Fractals
be chaotic. Exhibit kiosks, many of which are fractals, include Musicof the Heart, Frozen Lightning, Erosion, Viscous more .
http://mathforum.org/library/topics/fractals/?keyid=9511105&start_at=51&num_to_s
An Introduction To Fractals
Gives definition and explains the different types of formulas used. Includes illustrations and bibliography.
http://www.swin.edu.au/astronomy/pbourke/fractals/fracintro/

Extractions: May 1991 "Philosophy is written in this grand book - I mean universe - which stands continuously open to our gaze, but which cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth." - Galileo (1623) B. Mandelbrot A set of points whose fractal dimension exceeds its topological dimension. The classic Mandelbrot below has been the image that has greatly popularised chaotic and fractal systems. The Mandelbrot set is created by a general technique where a function of the form z n+1 = f(z n ) is used to create a series of a complex variable. In the case of the Mandelbrot the function is f(z
Archive Of Desktop Wallpaper
Free desktop wallpaper of animals, death, fractals, scenery, seasons, space, landscape, 3d, and other all are computergenerated images. Links to other sites with desktop wallpaper.
http://www.geocities.com/llaar6/
A Slice Of Pi
Digits, chronology, expressions, other constants, maths books, fractals, Rolling Stones lyrics, and computer games.
http://www.yxq98.ukgateway.net/
Free Photos And Images By Lemon Logix
Featuring Terragen rendered landscapes, fractals, textures, and traditional drawings.
http://www.geocities.com/lemon_dlf/
Fractal Morphing Screen Saver, Free EscapeClose, Game Hidden Swap Buttons, Launc
Fractal Morphing Screen Saver is a screen saver for Windows. Displaying morphing of fractals and has many adjustments.
http://www.sanapesoft.com/

Extractions: EscapeClose is an absolutely free tiny utility, allowing you to close the active window by pressing the Esc button. Or, to work more carefully, it can position the mouse cursor in the upper right-hand corner of the active window, where the Close button is located. It is especially useful when you are working with dozens of files and folders at once. Download free...
MaryannsArt.com : Home
Assortment of art, fractals, scenery, photos, clipart, wallpaper and panoramas by the web mistress.
http://www.maryannsart.com/cgi-bin/ImageFolio31/imageFolio.cgi
Fractals
Provides images, quotes and information on the different types of fractals.
http://astronomy.swin.edu.au/~pbourke/fractals/

Extractions: Examples of self similarity in fractals with examples from mathematics and photos of the physical world. I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images that illuminates our perception of art? Could it be that a fractal image is of such extraordinary richness, that it is bound to resonate with our neuronal circuits and stimulate the pleasure I infer we all feel?
Fractal Links
Fractal Bibliography (text); Fractal music URLs (text); Fractal URLs (text);More Fractal URLs (text); The Fractal music Project. mersenne numbers blank.
http://www.apu.ac.uk/music/rhoadley/links/links_fractals.html

Extractions: Or you could get Kai's Power Tools (version 6)as a plug-in for Photoshop if you use it.If you must have freeware then I suggest Fractal Zplot from: terry Other useful/interesting fractal links: www.fractalus.com www.crosswinds.net library.advanced.org Paul.N.Lee ... Juan Luis: Third.Apex.to.Fractovia Fractal Music Software from Fractovia Fractal Music Software Fractals MUSIC FROM CHAOS index SSEYO homesite Koan generative music software sequencer ... The Fractal Music Project mersenne numbers blank
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
Fractalier's Page --- Lifesmith Classic Fractals
Over 1,500 fractal data and imagery.
http://www.lifesmith.com/
Ecometry
Chaos theory is a popular name for the theory of Dynamical Systems (DS), mainly for nonlinear systems. The theory covers many aspects of the life of DS, all of them have the same characteristics, they were born, they lived and they died.
http://www.geocities.com/ecometry
Fractal Music (man )
Fractal music Last night a hot air balloon with a Colonel Sanders iconand the words Chook Satan , drifted across Sydney harbour.
http://www.octapod.org.au/s/fractalmusic.html

Extractions: Last night a hot air balloon with a Colonel Sanders icon and the words 'Chook Satan', drifted across Sydney harbour. Zooming in, if you'd climbed the bridge, you could see in the balloon, a little boy caressing a toy hot air balloon. An elaborate production for a Pink Floyd album cover? No, The 3D budget for technoscape just went up to include short film clip introductions, and Jean Poole thought this a great way to introduce fractal music. Fractals are the representations of complex mathematical formulae which exhibit certain characteristics, namely self-similarity across many scales, repeating patterns, similar, yet...slightly different. Fractal Music maps these outputs to the parameters that define music, midi instrument events, for example, to determine when a note is played, the volume, pan, which note on the scale, etc. Today's technoscape guest is Phil Jackson, from www.fractal-vibes.com

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