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

1. Don Archer Digital Art
Artist provides various galleries dating back to January 2001. Read a brief biography, and find suggested resources. vintage fractals, animations, ceramic tiles . enhanced digital photographs, digital postcards . Don's fractal music and
http://www.donarcher.com/
Monday, 4/7/2003 , 8:11:43 PM (EST), Brooklyn and Prattsville, NY
Updated April 4, 2003 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 10 viewers online now. Enjoy!
There's nothing for sale here.
Thanks for visiting! YEAR 2003
FRACTALS Gallery

April 2003
Gallery
March 2003
...
January 2003
YEAR 2002
FRACTALS Gallery
December 2002 Gallery November 2002 ... January 2002 YEAR 2001 FRACTALS Gallery December 2001 Gallery November 2001 ... ANIMATIONS Don Archer, director CREDITS
  • Online ABS gallery 2001-2003 hails Don Archer as "fractal guru" and publishes comprehensive exhibit of his 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.
  • Several one-man and group shows, NYC and internationally, 1994-2003.

2. Discovery Online - Fractal Music: The Sound Of Chaos
Faking It Alt TextAlt Text, Those who hear fractal music for the first time findit hard to describe more, The music Makers How do they do it and why?
http://www.discovery.com/stories/technology/fractals/fractals.html
Those who hear fractal music for the first time find it hard to describe ... otherworldly, bizarre, fantastic. It's part of a fractal universe full of startling sights and sounds. more
The Music Makers

How do they do it and why? Create Your Own Chaos
Fantastic Voyage

Enter a fractal image Hear What You See
A Fractal World

See and hear fractal sights and sounds
1999 Discovery Communications Inc.

3. Unusual Music At Unusual Research
"All of the music on Unusual Research is actually the musical representation of fractal equations .Category Arts music Styles Experimental Fractal music......UNUSUAL music. The music of fractals.
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

4. Fractals, Chaos, And Music
relations have been discovered in recent years between fractals and music. This paper will cover some of the research
http://www.geocities.com/SoHo/Square/7921/fmusic.html
Fractals, Chaos, and Music
Abstract
Many relations have been discovered in recent years between fractals and music. This paper will cover some of the research that has been done on these relations, including some of the controversies over conflicting discoveries. It will show how some artists are currently using fractals to generate the basic melodies in their compositions. A few computer programs which can be used to generate these melodies will be discussed. This paper will also examine possible practical uses for software which can be used to hear patterns in fractals. The algorithms behind the music-generating algorithms will be discussed, as well as some of the basic relations between mathematics and music. Some of the work of music theorist Joseph Schillinger, whose ideas in the 1920's and 1930's about generating music by recursive and chaotic means were far ahead of their time, will also be covered.
Historical perspective
The mathematical study of music is certainly nothing new, dating back to ancient Greece. Around the 5th century BC, the Pythagoreans formulated a scientific approach to music, expressing musical intervals as numeric proportions. This was probably done by observing the tones produced by plucked strings of different lengths; for example, the tone produced by a string held at the middle is an octave higher than that of the whole string. They went on to calculate the intervals for several different scales, including the chromatic and diatonic scales. Archytas of Tarentum, a Pythagorean mathematician who lived around 400-350 BC, was even able to work out the relationships between notes in the enharmonic scale, which includes quarter tones. (Britannica)

5. Fantastic Fractals
Tutorials for all ages, fractalgenerated music and realistic landscapes. The Fantastic fractals 98 software is available for download. Workshop, message boards, and discussion forum.
http://tqd.advanced.org/12740/index.html

6. Discovery Online - Fractal Music: Create Your Own Chaos
Create Your Own Chaos Turn numbers into music. To make music withthis MusiNum, you'll need to be able to hear MIDI recordings.
http://www.discovery.com/stories/technology/fractals/create.html
Create Your Own Chaos Turn numbers into music. That's the aim of fractal fan Lars Kindermann, who created this computer program to do just that. By plugging in numbers, choosing instruments and selecting the scale and other musical settings, you can hear fractal music of your own making. To make music with this MusiNum, you'll need to be able to hear MIDI recordings. Some browsers do this automatically. Another way is to download QuickTime. Tempo beats per minute Length counts
Step
Base
Start
Octave Octave 1 Octave 2 Octave 3 Octave 4 Octave 5 Octave 6 Octave 7 Octave 8 Octave 9 Octave 10 Octave 11 Octave 12
c #c d #d e f #f g #g a #a b
Major Minor Penta Twelve
Legato Pedal Staccato
changed Notes play all Notes only same Notes
Grand Piano Bright Piano Electric Piano Honky-tonk Piano Rhodes Piano Chorused Piano Harpsichord Clavinet Celesta Glockenspiel Music Box Vibraphone Marimba Xylophone Tubular Bells Dulcimer Hammond Organ Percussive Organ Rock Organ Church Organ Reed Organ Accordion Harmonica Tango Accordion Acoustic Guitar (nylon) Acoustic Guitar (steel) Electric Guitar (jazz) Electric Guitar (clean) Electric Guitar (muted) Overdriven Guitar Distortion Guitar Guitar Harmonics Acoustic Bass Electric Bass (fingered) Electric Bass (picked) Fretless Bass Slap Bass 1 Slap Bass 2 Synth Bass 1 Synth Bass 2 Violin Viola Cello Contrabass Tremolo Strings Pizzicato Strings Orchestral Harp Timpani String Ensemble 1 String Ensemble 2 Synth Strings 1 Synth Strings 2

7. ThinkQuest Library Of Entries
A site devoted to covering many different aspects of fractals, such as mathematics, music, applications, image compression, and advanced math.
http://library.advanced.org/25810/
Welcome to the ThinkQuest Internet Challenge of Entries
The web site you have requested, Our Fractal Universe: Mandelbrot and More , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Our Fractal Universe: Mandelbrot and More click here Back to the Previous Page The Site you have Requested ...
Our Fractal Universe: Mandelbrot and More
click here to view this site
A ThinkQuest Internet Challenge 1999 Entry
Click image for the Site Languages : Site Desciption
Students
Jason Lafayette High
MO, United States Ben Lafayette High
MO, United States Coaches Bo Diversified Consulting Resources, Inc.
MO, United States

8. Fractal Music Lab
Tools and information on exploring and advancing the musical use of fractals. With sound samples, software, and articles on fractals and composition.
http://www.fractalmusiclab.com/

9. Digital Fine Art By Brian Evans: A Gallery Of Limited Edition Prints Of Visual M
Visual soundscapes, frozen music, unique fractals and computer graphics as available as original, limited edition art prints.
http://www.brianevansart.com/

Museum of

Computer Art

network site
1655 North McFarland Blvd., PMB 122, Tuscaloosa, Alabama 35406
205.750-0129 fax 205.343-4327
brian@lightspace.com

10. 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.

11. Unusual Music Friends And Associates
downloaded from his site. He is also an accomplished artist. Don Archer'sFractal Art And music And UDraw fractals. Don helps you create
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.

12. Digital Fine Art By Brian Evans: A Gallery Of Limited Edition Prints Of Visual M
Digital Fine Art Gallery. Visual soundscapes, frozen music, digital abstracts, unique fractals and computer graphics art available as originals and limited edition prints.
http://www.lightspace.com/finearts/evans.html
1655 North McFarland Blvd., PMB 122, Tuscaloosa, Alabama 35406
205.750-0129 fax 205.343-4327
brian@lightspace.com

13. Sprott's Fractal Gallery
Daily updated gallery of automatically created fractals. Fractal generating software.Category Science Math Chaos and fractals Fractal Art...... MIDI Fractal background music courtesy of Forrest Fang Fractal of the Day. Olderfractals of the Day are saved in an archive, which you can access.
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.

14. Digital Fine Art By Brian Evans: A Gallery Of Limited Edition Prints Of Visual M
Visual soundscapes, frozen music, digital abstracts and unique fractals and computer graphics art available as original prints in limited editions.
http://www.lightspace.com/

Museum of

Computer Art

network site
1655 North McFarland Blvd., PMB 122, Tuscaloosa, Alabama 35406
205.750-0129 fax 205.343-4327
brian@lightspace.com

15. Fractals
in denying the possibilities of actually using fractals in music while admiring the PeitgenRichter pictures for their
http://www.notam.uio.no/~rolfwa/Fractalarticle.html
Rolf Wallin:
Fractal Music - Red Herring or Promised Land?
or "Just Another of those Boring Papers on Chaos"

Lecture given at the Nordic Symposium for Computer Assisted Composition
Stockholm 1989
(Oops - seems that the references to illustrations don't refer to any illustrations... sorry...)
If the Vietnam war was the first TV war, the so-called Chaos theory must be the first commercially available scientific revolution, brought to a large public step by step. Chaos, fractals, Mandelbrot Sets, strange attractors, Cantor dust - these and some dozens other magical words have totally invaded popular science magazines during the 80's, accompanied by glossy colourprints of strange, disturbingly organical computergenerated shapes.
However, this is just the shiny facade of a revolution that has left the international community of scientists of most diciplines at first totally dumbfounded by seeing central parts of their theoretical basis crumble, then completely frantic to investigate to what extent these scientific Columbi eggs can be applicable on their particular field. Fluid mechanics, geology, medicine, meteorology, in most fields many unsolvable problems have been solved by applying some part of this manyfaceted and bewildering bag of theories. Visual artists has also been attracted by the organical shapes that appear on the computer screens.
So how about Music? Will fractal mathematics come to rescue in a time of apparent stagnation, this time in the guise of simple mathematical algorithms that yield delicious patterns that can be further processed, either as succession of musical events or as complex frequency spectra? The attempts to find an answer to this has barely begun. In the field of music the answers are not as selfevident as for the visual field. But this can actually turn out to be an advantage, if not technically, then at least aesthetically.

16. 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

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17. HOLONOMY AND FRACTALS ON MUSIC: HOLOFRACTAL MUSIC AS A SEMIOSIC SYNTHESIS
Holonomy and fractals in music. Holofractal music as a semiosic synthesis. Schroeder,Martin. fractals in music in Clifford Pickover, Fractal Horizons.
http://www.geocities.com/absbsemiotica/holofrac.htm
Holonomy and fractals in music
Holofractal music as a semiosic synthesis
Eufrasio Prates Paper presented to the
VII International Congress of Semiotics
However, when we talk about contemporary music people tends to expect some expertise from the public to "understand" the music. As I conceive it, music is a phenomenon to be felt, before being rationally understood. Of course there is no clear division between emotion and reason. Their role in the living experience of music is largely a complementary one and follows that every human being is capable of that. For this reason, I assume that contemporary music has a very special function today: to carry the most relevant ideas, changes and discoveries of our time to every human being willing to that. This first topic leads us to the next: what are those mentioned ideas, changes and discoveries? Of course each composer makes her/his choices. My choice was to keep only the paradigmatic ones. As the biggest changes of this century appears to be founded on the discoveries of the new physics, I have made a research of them, which is summarized at the article Música Quântica: em torno de um paradigma holonômico Quantum Music: around a holonomic paradigm Holonomy and fractals Most will agree that the quantum behavior of matter is one of the main discoveries of this century. As a matter of fact, the Bell Theorem proves mathematically that separated and distant parts of the universe are connected in an intimate and immediate form.

18. Fractal Images By Sharon Webb - Home Page
Galleries, 3D Art, and music.
http://www.fractalus.com/sharon/home.htm
The images on this page should be viewed in hi-color or truecolor settings.
Click on the purple links to enter the galleries. Sterling Fractals Fractals II Created 12/19/01 Fractals I Created 12/18/01 XenoDream Images Fractals Created 12/19/01 Animals Created 12/19/01 Sketches Created 12/19/01 Ultra Fractal Images Ultra Created 12/20/01 Slide Show Created 12/20/01 Fractalscapes Fractalscapes IV Created 12/21/01 Fractalscapes III Created 9/13/98 Fractalscapes II Created 9/13/98 Fractalscapes I Created 8/03/97
Moods and Faces Moods II Created 12/21/01 Moods Created 9/19/98 Animations Created 12/23/01 Galleries, Java Applets, Downloads Page II
Order Prints Order Information
Buy shirts and more at the FractalShop Visit FractalShop
Sorry!
"Fractal Dance" MIDI © Sharon Webb, 1998.
All images © Sharon Webb, 1997-2001
For print availability, contact Sharon Webb For more information about the art or music on this site, click here For Site Awards page, click here
This page was created 2/15/97.
This page was updated on 1/3/03. If you have questions or comments for Sharon Webb, click

19. 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

20. Hidden Dimension Fractals
Ron Barnett's fractal images, music, raytracing, Ultra Fractal formulas and links.
http://www.hiddendimension.com/
Floral Array Fractal of the Week January 1, 2003
Click on the image to see it full size.
  • Ultra Fractal Galleries Truemand Galleries Fractint Galleries Ray Tracing Gallery ... Links
  • To email me, click here Fifth Place, 1997
    Fractint Contest
    Stream in the Forest First Place, 1998
    Most Whimsical Fractal
    Howdy, Earthling Third Place, 1999
    Easter Egg Coloring Contest
    Dragon Egg First Place, 1999
    Organic
    Tree of Life First Place, 1999
    Animation Birth of the Phoenix Return to Top

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