Re: Variance is Fractal
A straight line meets more of the fractal criteria than a variance (deviation from sklanskybux) vs. #hands plot. Weak statistical self-similarity (expected value of point n+x is always the value of point n, for all x.. which is also true for a horizontal line) isn't particularly interesting. If you have a more interesting metric for variance vs. hands that's scale-invariant (and doesn't explicitly use scale in its calculation), I'd be curious.
A 1-d plot of possible deviations from sklanskybux (if the point has been traveresed, it exists), which is just a 1-d random walk, is self-similar because it's just the discrete analogue of a straight line (which is completely uninteresting).
Brownian motion is more interesting because it's 3D, and a random walk in 3D does NOT almost surely cover all points (a 1-D random walk, which variance is, does), so the points covered make a nicely irregular fractal shape.
|