| Most of the fractals we have seen, both mathematical and natural,
are generated by some dynamical process. For example, |
| IFS
generate fractal by iterating a collection of transformations, |
| fractal coastlines
grow by long-term erosion from wave action, and so on. |
| Yet usually we see just the final product, not the process. |
| Cellular automata make the time-dependence more obvious: time records of some CA are fractals (with the
gasket appearing frequently - no surprise here). |
| We discuss three different kinds of noise and describe a CA experiment
searching for 1/f noise. |
| A first tool in analyzing noise is the
power spectrum. |
| The simplest is white noise: a
monkey banging on a piano, each note is unrelated to what came before. |
| Opposite this is Brownian noise: a
cat chasing a moth across a piano, each note is based on the previous note, but the change in
notes is unrelated to the previous change. |
| Midway between these is 1/f noise.
|
| Interestingly, Richard Voss found 1/f characteristics in almost all
music. |
| Though there is no general agreement about the mechanism producing 1/f noise,
there are some attempts at explanation. |
| Finally, here is an experiment testing the relation between 1/f noise and
complex CA. |
|