The Hurst statistic, converted easily into a fractal dimension, quantifies the degree of clustering of high and low values in spatial or temporal series of data. In an effort to better understand the stratigraphic organization of submarine-fan deposits, the Hurst statistic was calculated for nineteen turbidite sections that span a wide range of geological time, tectonic settings, facies characteristics, and depositional environments. Three bed-by-bed variables were considered: coarse-division thickness (i.e., net thickness, in a single bed, of conglomerate+sandstone+siltstone), grain size, and coarse-division thickness percentage (relative to thickness of overlying mudstone caps). Sixteen of the 19 turbidite sections analyzed (84.2%) show the Hurst phenomenon, i.e., irregular, long-term clustering of high and low values of the three bed-by-bed variables. This clustering is related to stratigraphic changes of sedimentary facies caused by lateral shifting of sub-environments on a submarine-fan surface. There is no evidence that the clustering is controlled by sea-level fluctuations. The strength of the clustering, inferred from Hurst K values, holds promise as an index to distinguish submarine-fan sub-environments. Preliminary results suggest that channel-levee deposits tend to have strong clustering; lobe-interlobe deposits tend to display moderate clustering; and basin-floor sheet-sand systems tend to have weak clustering. Combining facies characteristics with these statistical results provides more reliable criteria for the identification of submarine-fan sub-environments than are available from recently discredited models based on asymmetric cycles of bed thickness or grain size.