The use of fractals to quantify the morphology of cluster microforms

The emphasis of this paper is on the fractal-analysis of irregular objects like particle clusters that fill the two-dimensional Euclidean space R2. A common fractal descriptor of such objects is DL (1   5, pseudo-triangle, and -rhomboid. The analysis for this study is performed by applying the box-counting method for analyzing cluster planview images from four groups of cluster morphologies derived from synthetic, laboratory, and field data sets. The DAT is determined via Richardson plots by estimating the slope of the best-fit line over the entire range of box sizes. Doing so, provides a single aggregate dimension that includes the embedded effects from the objects projected area and perimeter. The results show that the average DAT¯ and its standard deviation can effectively discriminate the four cluster morphologic groups. The DAT¯ provides a clear demarcation between the nonlinear morphologies and the in-line morphology with ER > 5. The analysis also shows that the in-line clusters with ER < 5 change between pseudo-linear and pseudo-nonlinear morphologies. Moreover, it is found that most morphologies in the field are statistically well represented by the corresponding laboratory and synthetic morphologies. Finally, the analysis of the laboratory cluster data reveals the utility of DAT¯ for portraying the correspondence between cluster morphology and physical processes responsible for cluster formation and morphologic evolution, such as flow and sediment supply. Future research should build on the knowledge gained on this topic and further examine the links between the fractal dimension of different cluster morphologies and the physical processes that produce the characteristic scale captured by DAT¯.

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