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Diffusion-limited aggregation
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Diffusion-limited aggregation is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witt
A DLA cluster grown from a copper sulfate solution in an electrodeposition cell
A DLA cluster grown from a copper sulfate solution in an electrodeposition cell
A DLA obtained by allowing random walkers to adhere to a straight line. Different colors indicate different arrival times of the random walkers.
A DLA obtained by allowing random walkers to adhere to a straight line. Different colors indicate different arrival times of the random walkers.
A DLA consisting of about 33,000 particles obtained by allowing random walkers to adhere to a seed at the center. Different colors indicate different
A DLA consisting of about 33,000 particles obtained by allowing random walkers to adhere to a seed at the center. Different colors indicate different arrival times of the random walkers.
High-voltage dielectric breakdown within a block of plexiglas creates a fractal pattern called a Lichtenberg figure. The branching discharges ultimate
High-voltage dielectric breakdown within a block of plexiglas creates a fractal pattern called a Lichtenberg figure. The branching discharges ultimately become hairlike, but are thought to extend down to the molecular level.
Fractal dimension
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In geometric measure theory, fractal dimensions enable consistent statistical indexes of complexity in patterns. Since fractal patterns can be scale-variant, measuring space-filling capacity should be
Diffusion-limited aggregation
…dimension of approximately 1.71 for free particles that are unrestricted by a lattice, however computer simulation of DLA on a lattice will change the fractal dimension slightly for a DLA in the same embedding dimension. Some variations are also observed depending on the geometry of the growth, whether it be from a…
Figure 2. A 32-segment quadric fractal scaled and viewed through boxes of different sizes. The pattern illustrates self-similarity. The theoretical fr
Figure 2. A 32-segment quadric fractal scaled and viewed through boxes of different sizes. The pattern illustrates self-similarity. The theoretical fractal dimension for this fractal is 5/3 ≈ 1.67; its empirical fractal dimension from box counting analysis is ±1% using fractal analysis software.