Instructions - Diffusion Limited Aggregation Calculator

Purpose:

This calculator creates an aggregate crystal from individual particles using a Diffusion Limited Aggregation process. It allows for lattice based DLA aggregates using square, hexagonal, and octagonal lattices. Users can modify sticking probabilities and compute the fractal dimension of an object using a box counting method.

Building Aggregates:

Create aggregate makes a fresh seed particle with no attached particles, ready for you to build a new aggregate.

Set the details for your screen geometry before creating a new aggregate. Screen size and geometry changes do not take effect until the next time you create a new aggregate.

You can build your aggregate either one step at a time, or you can run up to some size limit.

You can change your sticking probabilities at any time by pressing the sticking probabilities button.

Sticking Probabilities

You have the option between a simple sticking probability or individual probabilities based on the number of neighbors.

When using the advanced sticking probabilities, you can set separate probabilities for sticking to a single particle based on whether you are continuing a straight line of bonds or not.

Computing Fractal Dimension

When computing the fractal dimension, you can select an area of the screen or you can leave the screen unselected to use the whole screen.

The fractal dimension is calculated using a box-counting method. In a box counting method, successively finer resolution meshes are laid over the image being measured. The number of boxes that overlap with the image are counted. For a perfectly 2 dimensional object, as the mesh resolution increases, the number of boxes in the mesh that are filled should go up in proportion to the mesh resolution squared. For a line, it will be proportional to the mesh resolution. For a DLA fractal, the result is typically that the number of filled boxes increases as the mesh resolution to some power that is neither 1 nor 2. This power is the box counting fractal dimension.

A simple way to measure fractal dimension using this method is to plot the log of the number of filled boxes against the log of the mesh resolution. The slope of the resulting line is the box counting fractal dimension. Apply the box counting technique with different mesh resolutions, and as you do a plot of filled boxes vs. mesh dimension will be created for you.

Click and drag on either end of the line in the plot to place the line on top of the data. The slop of the line will be displayed.