fractal techniques, another strange attractor (Henon)
Lindenmayer systems
video of this class
We invetsigated two model/equation systems that presented some interesting
challenges for data sonification. Instead of interpreting a simple
recursive fractal system as pitches, we used it to generate time-points
for a rhythmic figure. Next we noticed that the
Henon attractor scatters points onto the
attractor as it is generated, and if you simply sonify them directly
it will sound like semi-random pitches. So we scanned through the
attractor as it was being produced.
We didn't do any direct L-systems coding, but we looked at several
examples of how they can generate elegant and beautiful pieces of
music. There are lots of examples "out there" in the world.
Links
There are many good web sites devoted to fractals, strange attractors/chaos,
L-systems, etc.
Googgle these terms and you will find them! Here are just a few I used for
class.
strange attractors/the Henon attractor
- Paul Bourke's web page
-- this is the site with all the equations for various
chaotic/fractal/etc. techniques. It has the code for the Henon
attractor that we used.
- trange Attractors: Creating Patterns in Chaos
-- a book (Luke Dubois recommended) by Julien Sprott; a comprehensive
look at strange attractors
- older class link
-- some good links on this to attractor info (a number no longer work,
I'm afraid)
- even older class link
-- good picture of a Henon graph with some info (the same page
I referenced for the logistic map/population equation and the
Lorenz attractor)
fractals
- older class link
-- A different use of fractals (to generate delays), the code is old
but it was interesting to hear the results. Most of the links on this
page no longer work
- a not-so-older class
-- L-systems and fractals. Looks like a lot of the links here seem to
work.
- Profiles
-- the fractal piece by composer Charles Dodge I played in class
L-systems
- L-systems app
-- you can alter the string, the graphics interpretation parameters,
etc. Some good examples as starting-points.
- fractal/L-systems interactive app
-- shows the 'fractal' (recursive) aspect of some L-systems
- yet another L-systems app
-- this one is fun because it animates the calculation/drawing of the
L-system.
- Luke Dubois' doctoral dissertation page
-- includes the
dissertation itself
along with links to the videos/pieces he made as part of his project.
- Vanishing Trajectories
-- the piece that Akira Takaoka made with laser artist Keiichi Tanaka
using L-systems
- Akira's explanation
-- some text about how Akira used L-systems to generate the music.
Class Downloads