A common technique for studying the influence of uncertainty and error on a
mathematical model involves the use of what is termed "noise".  The most common
choice is white noise, for which the values at x(i) and x(j) are independently
sampled from an underlying Gaussian or uniform distribution.  The construction
of the white noise function implies that the power spectrum is a constant
function of frequency, however, this leads to properties that don't always
agree with experimental data or other observable features.

Alternatives to white noise have been proposed; in particular, a family of power
law noise functions, leading to what is called correlated or colored noise.
For colored noise, we assume that the power density spectrum of a noise signal
can be modeled as 1/f^alpha, where alpha is a a parameter that is chosen based
on problem-specific considerations.  We study a method for generation of
discretized colored noise for various choices of alpha and we analyze the
effects of the resulting noise on the solution of partial differential
equations.