- a good set of java apps -- including the "Fractal Microscope"

- simple fractal tutorial
-- and the base page
has some interesting math tutorials and models, fairly basic though

- NCSA fractal home page -- the folks who made the "Fractal Microscope"

- fractal music links -- including a link to fractal vibes. Too bad about the annoying commercials on this site for products you probably don't want or need.
- Gary Nelson's web page -- the king of fractal music
- basic fractal music bibliography

- the fractal music project -- this has one of the most annoying color-schemes I've seen on the web in awhile...

- G6610 older class
-- this has a good disussion (with purty pictures even!) of
the "fractal reflection" exercise we did in class. Again, some
of the links are a little old... the link to the RTcmix
STEREO
instrument documentation is older, and
use the
*xmountains.tar.gz*package linked below here for Mac OSX. - reflect.tar.gz -- the code for our 'fractal reflection' exercise (described in the "G6610 older class" link above)
- mandel.tar.gz -- the Mandelbrot set application, zoom in and realize as a frequency vs. time graph (decribed briefly below)
- xmountains.tar.gz -- Mac OSX (under X11.app) version of the fractal mountain-making program. I think this will also compile ok on Linux "as is", otherwise visit the "G6610 older class" link above for the Linux version.

The first thing we did in class was to play some examples of

One thing to keep in mind with a lot of these algorithmic topics is that
many of them are related. For example, when we discuss L-systems later
in the term, they are often seen as a good example of a procedure which
can generate a fractal boundary (basically a fractal has a 'fractional
dimension' as defined by Benoit Mandebrot in his class book * The
Fractal Geomtery of Nature* -- a "wiggliness" that causes the boundary
to lie between two dicrete measure of dimension. For example, an infinitely
crinkled line can't really be thought of as lying entirely in 1 dimension,
but it really isn't a 2-dimensional object either; a fractal).

Next we looked at a simple little application that graphed the Mandelbrot set (shown in basic form above). The Mandelbrot set is generated using the simple-looking equation

We can make a more dramatic-looking graph by measuring how quickly points outside the Mandelbrot boundary go to infinity and using this to change the coloring of each initial point:

Adding the ability to select an "zoom in" to different sections of the Mandelbrot set (like the Fractal Microscope) allos us to generate a wide range of different images:

As with the Henon attractor application in last week's fun, we can interpret these images as extended frequency/time graphs. The brightness of the color of each pixel represents the amplitude of the particular frequency mapped to that pixel row.

Here are several example sounds created by interpreting the horizontal axis as time (25 second span) and the vertical axis as frequency (70 Hz -- 2570 Hz):

- mandelsound1.mp3 -- mono interpretation
- mandelsound1a.mp3 -- stereo interpretation of the same region (randomized location in left-right field for each grain)
- mandelsound2.mp3 -- stereo interpretation of a different region