ilon_t + \omega_t\sqrt{1 - k^2}\)</span></p>
<p>Mathematically, we can also think of unautocorrelated stochasticity as random sine waves evenly distributed across all wavelengths, while autocorrelated stochasticity is biased either toward sine waves of long wavelengths (red) or short wavelengths (blue).</p>
<p>Expressed graphically, colored noise looks like this:</p>
<p><img src="noise_files/figure-html/comparing%20red%20and%20blue%20noise-1.png" width="700"><img src="noise_files/figure-html/comparing%20red