The recognition of fractal structure in stratigraphic systems is becoming increasingly widespread. Within the plethora of scale-invariant sedimentary structures, stylolites are one of the most visually suggestive of fractal form. Traces of stylolites, viewed in vertical section, have been studied by standard Fourier spectral analysis and are found to possess spectra typical of 1/f fractional noises. The power distribution is significantly shifted towards the low-frequency end of the spectrum. This red-shifted spectrum is best modeled as a persistent fractional noise. Such noise spectra are those where successive positions along the data series, in this case the trace of the stylolite, are strongly positively correlated. Therefore, stylolites are readily modeled as strongly persistent Brownian trails. Regression of the noise spectrum shows the fractal dimension of the stylolite trace to be 1.346.