Five Cellular Automata:
Diffusion-Limited Aggregation
This is a computer simulation of a process known as diffusion-limited aggregation.

Initially a grid is occupied randomly by cells in a certain concentration, e.g. 25%. One or more of these are "seed" cells, which are visible, do not move and are (usually) colored white. Cells which do not move are called "fixed" cells. The cells other than the seed cells are initially "mobile" and perform a "random walk", i.e., they move repeatedly from their current location to any immediately-adjacent empty location chosen at random. Mobile cells are not visible.

When a mobile cell, by means of its random motion, comes to occupy a location immediately adjacent to a fixed cell then it too becomes fixed and also becomes visible, with a certain color, not necessarily white. Some mobile cells may disappear if they stray too far from the center. The process continues until all mobile cells have either disappeared or have become fixed cells.

When there is just one seed cell, at the center of the grid, this process results in the formation of a structure such as that shown below left. When there are multiple seed cells we get something like what is shown below right.

The initial screen for the Diffusion/Aggregation automaton has controls as shown at right:

The rules for this automaton are given on the Algorithms page.

Here's an example of what the system looks like after running awhile, beginning with one seed cell, a concentration of 25% and using eight colors:

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