Regular fractal aggregates

Figure 14.4. Regular fractal aggregate constructed in two dimensions (d = 2) and in three dimensions (3d). The aggregate d = 3 (b) is shown along its principal diagonal The fractal dimension of such an object is D = Log (2d + l)/Log 3 [JUL 87]...

We focus on aggregation in model, regular and chaotic, flows. Two aggregation scenarios are considered In (i) the clusters retain a compact geometry—forming disks and spheres—whereas in (ii) fractal structures are formed. The primary focus of (i) is kinetics and self-similarity of size distributions, while the main focus of (ii) is the fractal structure of the clusters and its dependence with the flow. 

Figure 3. The logarithm of the standard deviation is plotted versus the logarithm of the average value for the heartbeat interval time series for a young adult male, using sequential values of the aggregation number. The solid line is the best fit to the aggregated data points and yields a fractal dimension of D = 1.24 midway between the curve for a regular process and that for an uncorrelated random process as indicated by the dashed curves.

Figure 8. The aggregates composed of 50 (top) and 100 (bottom) CPs used in the model calculations. The first two are regular and have a tetrahedron lattice, the others are random fractals with different packing parameters (see text for details). The fractal dimensions, prefactors, and gyration radii (for 100 CPs) are shown in the footnote.

One important conclusion can be made the spatial disposition of particles in floes results from the biopolymer/particle concentration ratio in addition to the biopolymer conformations. In particular, flocculation processes with rigid biopolymers resulted in the formation of a regular network characterized by fractal dimensions that were higher than those obtained on the basis of the classical DLCA or RLCA models (Figure 4.16). Despite the highly loose structure of the aggregate that was formed, the increase in fractal dimension reflected the high order of particles in such networks. 

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