Photo: Lara Sobel plays with naturally-synthesized fractals by burning into wood via high voltage.

Fractals, those wacky self-similar, rough geometries that resemble so many patterns in nature, were once all the rage. Ravers and digital artists embraced them, only to get bored with them, apparently. To billions of years of evolution and natural phenomena, they’re still cool. And to me, there’s still plenty to talk about when it comes to thinking how fractals might be all the rage.

Composer Terran Olson, a musician with a long resume that includes work with the Ives Quartet and Quartet San Francisco, takes on the idea of fractals in a new article. Writing for our friends at Rain Pro – makers of music and visual pro PC laptops – Terran explores how fractal patterns could be applied to sound.

Exploring Audio Fractals

The results are fascinating: they’re a kind of fractal synthesis. Of course, that gets at the heart of the question: just how do you map a visual pattern like a fractal – or anything else visual – to music? The answers aren’t always intuitive. The biggest question is whether to work at the scale of sound (Terran focuses on individual samples and impulses), or to deal with musical patterns. I knew I had read a fractal article in Electronic Musician; sure enough, in 1999 EM did a story on fractals that focused instead on pitch mappings. (Bonus: Bach even comes up.)

Fractals and Music

Composer Gustavo Diaz-Jerez penned that story, and the results tend toward algorithmic music. Many of the tools are now gone, though some survive (Csound) and other tools (Max/MSP, Pd, SuperCollider, Reaktor, ChucK) could certainly fill in.

And, of course, for a truly high-level musical approach to fractals, skip the individual sounds or individual notes and write a whole song, like Jonathan Coulton’s brilliant fractal ode, “Mandelbrot Set.” (It should also help anyone needing to, erm, brush up on their fractal theory.)

Sadly, neither of these articles is especially useful as how-to – great on theory, but not so practical if you haven’t tried these things before. That begs for a new tutorial. Are you working with fractals these days? I’d love to hear what you’re doing.

  • carlsbad

    Metasynth is another option for fractal-based music making.

  • http://www.createdigitalmusic.com Peter Kirn

    @carlsbad: Indeed — and offers a novel approach to mapping image to sound, as well.

  • http://fractaldimensionproductions.com Fractal Dimension

    I'll definitely keep my eyes on this topic, to do my name justice. :)

  • http://rucyl.com rucyl

    i've thought a lot about incorporating fractals into music but never got to it.. hmm may be a good weekend project

  • grimley

    For any Nord G2 users … there's a boatload of fractal patches over on the electro-music forum most of them by a bloke called JLS. For instance:

    http://electro-music.com/forum/viewtopic.php?high

  • http://www.institutfatima.org paul rose

    I used Musinum when I was on a PC. This is very 1999, but the article on the homepage is explaining the approach very well.

    For my mac I built a patch in pd that does the same stuff basically – outputting generative fractal midi.

  • http://stimulant.io Josh

    "just how do you map a visual pattern like a fractal – or anything else visual – to music?"

    Well, it's a mathematical pattern, not a visual pattern. It's just typically expressed visually. Music == math, much of the time, in at least western/popular music.

  • Jaime Munarriz

    There's an interesting tool called Softstep, a Modular environment for generating and manipulating midi data, that has built in fractal generators, modules where you can see the fractal image and use it as a midi data generator.

    The author makes music with protein's dna, and they have some tools for adapting this kind of biodata.

    I paid for the first version, and got some nice patches running.

    Their new tool is called Artwonk, and it also generates graphics…

    Their web: http://algoart.com

  • Jaime Munarriz

    The interesting thing on fractals and music is to play at several levels, from micro to macro structure. So you can think on micro-events, then parts, then form, all of them developing from a common generator. It's not easy to deal with, but you can find quite interesting music while trying.

  • http://nickkent.net nick kent

    My view is that this direction of exploration, at least on the surface is interesting to a degree but literally not going anywhere. Regarding fractals, when mapped to music in some way they they can create some interesting musical texture for moments but never a very interesting composition per se. Their self-similar nature brings some moments or ambient backgrounds of musical texture that don't go anywhere since there is no progression, just mild variation. The self similarity does work on a macro scale because in time one comes to realize progression or any real form won't happen. But maybe someone does want that as a goal. More power to them

    I'm not terribly impressed with any promise of graphics into music per se either. One is taking a space dimension, say width and saying that is equal to time. I'm not convinced that cuts it when making a claim, it's abstracted beyond an analogy. Though one can always get attention by saying "want to hear what this image sounds like" as if that was actually happening. Images don't intrinsically have a time dimension unless they are moving images.

    On the other hand I'm all in favor of one aspect of MetaSynth. The ability to encode sound into a graphic and then manipulate it with graphic tools is great. I wish their engine was more accurate as to what goes in comes back out sounding much like it should, but still it's a good tool.

  • Ken Marsley

    4/4 house or techno rhythm tracks have implications similar to the visual representation of the cantor set. Think of snare hits on the 2nd and 4th beats, and then the weight of bars 2 and 4 (and then 6 and 8) in a straight 8-bar phrase.

  • http://www.zacharyreese.com thesimplicity

    Ben Schachter released an amazing album called "Fractals"… it's basically generative jazz. It's VERY interesting what you realize what's going on structurally. Each song is sort of a section of the previous track, but magnified and focused, until it comes back around to the original track. It's very crazy.

    http://cdbaby.com/cd/schachter

  • http://wowcool.com/engine Marc Arsenault

    Back in 1999 again. Yo Kubota was the man with his Mandelbrot Music software. He seems to have dropped from sight. I remember it being pretty cool, but little else. There's a few examples of the midi he generated on this page: http://www.texaschapbookpress.com/magellanslog48/

    Googling fractal music seemed to time warp straight to '99 on every hit.

  • Luke

    Fractal behavior isn't just a visual phenomena; our heartbeat rhythms show fractal behavior in how they vary. The so called "Drunk Walk", or random brownian motion is related to the fractal behavior that produces coastlines and clouds.

    I devoted one section of my thesis to applying fractal behavior to music analysis of improvised music, and it contains an overview of fractal scaling behavior. It's online at
    http://ccrma.stanford.edu/~lselden/ (pg. 21)

    Other people that have used fractal analysis for music include Sebastian Streich, who uses fractal scaling behavior as a way to measure the "danceability" of songs in his thesis, and Jafari et all who analyze Bach (both cited below).

    I think fractals show up in music much more often. As Ken Marsley suggests above, any music that has some heirarchical structure in which multiple levels (bar, phrase, section) share some rules or tendancies has a fractal dimension (see http://en.wikipedia.org/wiki/Hausdorff_dimension).

    References:

    Streich, S. “Music Complexity a multi-faceted description of audio content.” 2007.

    Jafari, G. R, P. Pedram, and L. Hedayatifar. “Long-range correlation and multifractality

    in Bach's Inventions pitches.” 0704.0726 (2007). 15 Dec 2008

    .

    Peng C-K, Hausdorff JM, and Goldberger AL. “Detrended Fluctuation Analysis (DFA).”

    Fractal Mechanisms in Neural Control: Human Heartbeat and Gait Dynamics in

    Health and Disease. 15 Dec 2008

    .

  • http://www.raintone.com J.D. Northrup

    Peter, inspired by this article and Terran Olson's work, I dug into creating a more general version of the fractal set synthesis he outlines.

    I've posted the code, and some example .wav files on my site:

    <a href="http://raintone.com/code/genfractal/” target=”_blank”>http://raintone.com/code/genfractal/

    I'd love to see what other people can do with this stuff!

    Provide the rules and it generates recursive fractal sound based on it.

    For example, the arguments '1 101 000' lead to the following sequence:

    1

    101

    101000101

    … (ie the Cantor Set)

    You can provide any binary pattern you want, and it expands into a recursive fractal .wav file.

    Enjoy,

    -jd

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  • http://www.3amnoise.net/runagate runagate

    http://www.tunesmithy.connectfree.co.uk/

    This is the page for the wondrous and now quite hoary Fractal Tune Smithy which I used the free version of for a very long time and bought last year (I think I got the $35 version)

    "What's a Fractal Tune?

    There are many types of fractal, and one type consists of a triangle, with several smaller triangles added to each of its sides, and yet smaller triangles attached to each of those, and so on. The background of this page shows what it's like. It's called the Koch snowflake.

    So why not use musical notes, adding smaller notes within each one, and smaller ones within those, and so on.

    Or, easier in music, go the other way, and start with a small pattern and build it up to larger and larger structures."

    I also use it to re-tune multitimbral multiple-instances of VST plug-ins in microtonal .scala temperaments via MidiOx. Very, very useful and the developer is incredibly nice and very helpful. A legendary program!

    So that's another way of looking at fractals in music. And he has many a link to other projects there.

    Here's a link:

    <a href="http://www.google.com/url?sa=t&source=web&ct=res&cd=5&url=http%3A%2F%2 Fwww.kvraudio.com%2Fforum%2Fprintview.php%3Ft%3D214851%26start%3D0&ei=L7eySe35Nom-MoPyiOwE&usg=AFQjCNFc68UYbT8uYtGVA0kM65b8MFnITg&sig2=ajeLl-GUBTQUzVq5SyyjGQ” target=”_blank”>http://www.google.com/url?sa=t&source=web&amp…” target=”_blank”>Fwww.kvraudio.com%2Fforum%2Fprintview.php%3Ft%3D214851%26start%3D0&ei=L7eySe35Nom-MoPyiOwE&usg=AFQjCNFc68UYbT8uYtGVA0kM65b8MFnITg&sig2=ajeLl-GUBTQUzVq5SyyjGQ

    to a KVR thread, down for maintainance at the moment, linking to liqih's freeware Kaotica VST effect filter and midi chaos LFO

    have fun!

  • Aaron Urbanski

    From Veqtor's corner: Snowflakes

    Composed using Per Nørgård's fractal infinity series:

    a(2n) = -a(n), a(2n+1) = a(n) + 1, a(0)=0.

    Every four notes in the primary voice, the modus is transposed into a neighbouring one.

    It was made using Max/MSP, the Modal Objects Library by Vince Manzo and Fredrik Olofsson's f0.noergaard external. Sonically the voices are performed by Vember Audio's Surge. The glitch noises are from DEVSND's Arp 2600 and Bent 808 libraries, processed by DtBlkFx, Buffer Override and Reaktor.

    Tempo is 120180

    http://veqtor.blogspot.com/2009/03/snowflakes.htm

  • http://www.odesk.com/jobs/Sound-synthesis-website-create-simple-tone-sound-file-perhaps-generated-Fl Mark

    Could this project be of interest to any of you?

    I am looking to hire a deveoper. All offers and prices considered.

    It is a fractal sound synthesis for the web:

    http://www.odesk.com/jobs/Sound-synthesis-website

  • http://www.musicbeatmakerpro.com case

    I may be totally off my rocker here, but could somebody please explain to me the difference between a 'fractal' and a 'pattern' based sequencing device?

  • http://www.musicbeatmakerpro.com case

    I've worked in patter-based sequencers for years, and they seem to make the most sense (most intuitive) for me to use easily. Am I out of my league with this technology?

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  • Griff

    I’m not but I’m aware that near here at PLymouth University (UK) there are a little pocket of researchers working on applications of algorithmic music. On a cursory glance it looks like a guy called Alexis Kirke may be the one to get hold of. Good luck.

  • http://silverfang77.tumblr.com/ Silver Fang

    Sound is fractal. Sacred geometry is fractal. Are light and electromagnetic energy also fractal?