Random Growth Diffusion-Limited Aggregation: 2D Lattice |…

What is Diffusion-Limited Aggregation?

Diffusion-limited aggregation (DLA) is a process where particles move randomly until they come into contact with an existing cluster, at which point they stick and become part of the growing structure. This phenomenon was first studied by T.A. Witten and L.M. Sander in 1981.

The DLA model is particularly interesting because it can produce intricate fractal-like patterns that are self-similar across different scales.

How Does the Process Work?

In a diffusion-limited aggregation process, particles diffuse randomly in a medium until they encounter an existing cluster. When a particle comes into contact with the cluster, it sticks and becomes part of the structure.

The stickiness parameter controls how likely particles are to adhere upon contact; higher stickiness results in faster growth of the cluster.

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Applications and Observations

Diffusion-limited aggregation is observed in various natural phenomena such as electrodeposition, snowflake formation, and bacterial colony growth.

The resulting structures are often fractal-like, meaning they exhibit self-similarity at different scales, which can be quantified using the fractal dimension.

Real-World Examples

One of the most famous examples is the formation of snowflakes, where water vapor molecules randomly attach to an ice crystal lattice.

Another example is in the growth of bacterial colonies on a nutrient-rich surface, where bacteria spread and adhere to each other.

Frequently asked questions

What determines the shape of the DLA cluster?

The shape of the DLA cluster depends on the initial conditions (seed), the stickiness parameter, and the random walk of particles. Higher stickiness leads to a more compact structure.

Why is DLA important in science and technology?

DLA is crucial for understanding complex systems in nature and has applications in materials science, where it can influence the properties of composite materials and coatings.

Can DLA be used to predict natural phenomena?

While DLA models cannot perfectly predict specific events, they provide insights into the underlying mechanisms that govern the growth of complex structures, which can aid in understanding and predicting similar processes in nature.

How does bias affect the DLA process?

Biasing the random walk of particles towards or away from the cluster can significantly alter the shape and structure of the resulting DLA. This allows for a range of different growth patterns to be explored.

Try it live

Everything above runs in your browser — open Random Growth Diffusion-Limited Aggregation: 2D Lattice and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

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