Fano factor analysis was used to characterize the spike trains of single me
dullary neurons with sympathetic nerve-related activity in cats that were d
ecerebrate or anesthetized with Dial-urethan or urethan. For this purpose,
values (Fano factor) of the variance of the number of extracellularly recor
ded spikes divided by the mean number of spikes were calculated for window
sizes of systematically varied length. For window sizes less than or equal
to 10 ms, the Fano factor was close to one, as expected for a Bernoulli pro
cess with a low probability of success. The Fano factor dipped below one as
the window size approached the shortest interspike interval (ISI) and reac
hed its nadir at window sizes near the modal ISI. The extent of the dip ref
lected the shape (skewness) of the ISI histogram with the dip being smalles
t for the most asymmetric distributions. Most importantly, for a wide range
of window sizes exceeding the modal ISI, the Fano factor curve took the fo
rm of a power law function. This was the case independent of the component
(cardiac related, 10 Hz, or 2-6 Hz) of inferior cardiac sympathetic nerve d
ischarge to which unit activity was correlated or the medullary region (lat
eral tegmental field, raphe, caudal and rostral ventrolateral medulla) in w
hich the neuron was located. The power law relationship in the Fano factor
curves was eliminated by randomly shuffling the ISIs even though the distri
bution of the intervals was unchanged. Thus the power law relationship aros
e from long-term correlations among ISIs that were disrupted by shuffling t
he data. The presence of long-term correlations across different time scale
s reflects the property of statistical self-similarity that is characterist
ic of fractal processes. In most cases, we found that mean ISI and variance
for individual spike trains increased as a function of the number of inter
vals counted. This can be attributed to the clustering of long and short IS
Is, which also is an inherent property of fractal time series. We conclude
that the spike trains of brain stem sympathetic neurons have fractal proper
ties.