The slope of the log of power vs. the log of frequency in the arterial blood pressure (BP) spectrum is classically considered constant over the low frequency range, and is quantified by in the relationship "1/f." However, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine , are unclear. We present (1) data in rats (n=8) that reveal an extremely low-frequency spectral region (0.083 - 1 cycle/hr) where approaches 0 (the "shoulder") and (2) a model that (a) predicts a realistic value of within that range that conforms to fractal dynamics (~1-60 cycles/hr); (b) explains the shoulder; and (c) predicts that the "successive difference" in mean BP (mBP), is an important parameter. We recorded BP for up to 16 days. The absolute difference between mBP samples at 0.1 Hz (the successive difference, or ) was 1.87 ± 0.21 mm Hg (mean ± SD). We calculated for 3 frequency ranges: (a) 0.083 - 1; (b) 1 - 6; and, (c) 6 - 60 cycles/hr. for all 3 regions differed (p < 0.01). For the two higher frequency ranges indicated a fractal relationship (_6-60/hour = 1.27 ± 0.01; _1-6/hour = 1.80 ± 0.16). Conversely, the slope of the lowest frequency region was nearly flat (_{0.083-1 /hour} = 0.32 ± 0.28). We modeled BP as a random walk about 100 mm Hg with ranges above and below of 10, 30 and 50 mm Hg and with from 0.5 to 2.5. The simulated spectrum for the conditions mimicking actual BP resembled the observed spectra. We suggest that the mechanisms that limit the excursion of arterial BP (e.g., the baroreflex) produce the shoulder in the spectrum and that contributes to determining .