Links & Books

Works Cited & Other Places to Go...

"If in mathematics we treat nature a an analogy of art, in the greatest of music we treat art as an analogy of nature."
- Edward Rothstein

Fractal Music Sites

There are many sites out there which explain fractals, fractal music and the approaches to generate fractal music. These are my favorite sources online.

I confess that when I started this project, I was convinced that I was working on something completely unique. I did not know other folks were working on fractal music. When I found the Yahoo site listed below I was initially pretty bummed out... It popped my bubble... But the truth is that there is a lot of excellent work out there, and a lot of resources to bounce ideas and music off of...

Yahoo! Entertainment:Music:Computer Generated:Computer Generated Composition:Fractal Music - Many great links.
The Fractal Music Lab - Lotsa information on fractals, fractal music and fractal music software.
CNFractal_Music Forum - A forum specifically for fractal music. At the moment, it's almost all composers and programmers, which makes it a very valuable resource for sharing ideas and music.
Techniques for Algorithmic Composition of Music - One of my favorite papers on the subject. I stole both of my favorite quotes from this one. (Ada Lovelace & Brian Eno)
Recursion: A Paradigm For Future Music? - Another excellent paper.
Complexity and Artificial Life Concept - An intense, exhaustive site exploring chaos and complexity across a variety of fields. Equal parts academics and applied science.
Fractal Music Gallery - Literally an online gallery of Fractal Music artists' work.

Other Music Sites

There are thousands of excellent music-related sites out there. Rather than list scores of my favorite links that nobody will really follow, I decided to offer my short, short list of folks I know who are producing interesting music...

Thermal - Josh's disturbingly entertaining site. When I need a laugh, I visit & re-read the Mayonnaise List or the Electronic Salon. I aim to present some of my Fractal Music at the next salon. The salons really do exist. Honest.
IS Productions - Amy X Neuberg and Herb Heinz are an extremely talented pair producing fun, stimulating music. Music as mental cud you will find your gray matter chewing on long after you experience it. Actually, Herb is not particularly short.
Hmmm... - This is a band I was in a couple of years ago. You can follow the link and even listen to some MP3s. My guitar is usually unrecognizable as a guitar, so good luck. (There are two guitarists in the band...)

Recommended Books

Emblems of Mind - The Inner Life of Music and Mathematics, by Edward Rothstein. Rothstein casts his net very wide in an attempt to link mathematics and music. I do not think he is 100% successful, but this is the most articulate approach to the subject I've read that is accessible to the layman (e.g., me...). His exploration of the common ground between mathematics and music in an early chapter is an outstanding exercise in critical thinking.
Chaos - Making a New Science, by James Gleick. As has been typical throughout history in any significant endeavour, the people who advanced the science of fractals experienced resistance from the status quo, those who insisted that mathematics and mother nature did not behave the way they actually behave... This book is an excellent account of many key players, their contributions and the significant resistance they encountered despite the hard, cold facts they presented to the world... It's a surprisingly exciting book.
Chaos and Fractals - New Frontiers of Science, by Peitgen, Jurgens and Saupe. An exhaustive study of fractal shapes and the techniques used to generate them. An excellent reference book. I borrowed some plates from this book for use throughout this site.
An ABC of Music, by Imogen Holst. Uncluttered & concise pocket-sized reference book.
Music Notation - A Manual of Modern Practice, by Gardner Read. THE sourcebook for musical notation. Along the way, Read demonstrates how our ability to notate and record our musical thought were requisites for musical progress.
Godel, Escher, Bach: an Eternal Golden Braid, by Douglas R. Hofstadter. Even though I have just started reading this book as of this writing, I am overwhelmed and blown away.
Groo the Wanderer, by Sergio Aragones. The only truly required reading for any serious student of chaos. My Groo quote is from issue 88.
The Fractal Geometry of Nature, by Benoit Mandelbrot. Mandelbrot's classic book that tied it all together, gave 'fractal' its name and introduced a significant leap forward in mathematics. I borrowed some plates from this book for use throughout this site. Beautiful, challenging, mind-expanding and frustrating - like any truly worthy read!

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