  It has recently been observed that a stochastic (infinite degree of freedom)
time series with a $1/f^\alpha$ power spectrum can exhibit a finite correlation
dimension, even for arbitrarily large data sets. [A.R. Osborne and
A.~Provenzale, {\sl Physica D} {\bf 35}, 357 (1989).] I will discuss the
relevance of this observation to the practical estimation of dimension from a
time series, and in particular I will argue that a good dimension algorithm
need not be trapped by this anomalous fractal scaling. Further, I will
analytically treat the case of gaussian \onefas noise, with explicit high and
low frequency cutoffs, and derive the scaling of the correlation integral
$C(N,r)$ in various regimes of the $(N,r)$ plane. Appears in: {\sl Phys. Lett.
A} {\bf 155} (1991) 480--493.

Cellular Automata and Lattice Gases;Cellular Automata and Lattice Gases