Cellular Automata
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The Applets: Cyclic This rule is based on the idea of "rock, paper, scissors." A cell looks at its neighbors. If the cell is in state x and any of the neighbors examined are in state x+1, then the cell being considered changes it state to x+1, i.e. state x+1 "beats" state x. Also, state 0 "beats" the largest state, thus closing the "rock, paper, scissors" loop. Diffusion Limited Aggregation In this model, blue particles diffuse randomly; if a blue particle is ever adjacent to a green particle, it turns green and "sticks," or stops moving. Predator-Prey This spatial population ecology model allows you to investigate the effects of different spatial scales of activity for two species.

This page contains links to three of David Hiebeler's cellular automata Java applets. These applets are a visual representation of the type of mathematically based modeling on which Hiebeler's research is based. To see the applets, you need a Java-compatible browser.

You can think of a cellular automaton model as a piece of graph paper, with many small squares, called cells. Each cell can be one of several colors.

The squares are updated as follows: A clock ticks regularly, and on every tick of the clock (every "time step"), each cell examines its own value, and the values of some of its neighbors. It uses those values, and follows a kind of recipe or rule, which describes what its new state will be after the clock-tick. Every cell does this simultaneously, using its own value and the values of some of its neighbors, to compute their new value. They then all change their state to their new values, all at once.

It sounds somewhat abstract. But cellular automata models have been used for many things, from attractive screen savers to modeling phenomena in physics, ecology, biology, geology and fluid flow.

Click here for a detailed explanation of the controls.

The Controls

• From the "Array operations" menu, you can either choose "Clear" to set all cells to state 0, or "Random" to set each cell to a random state (all states having equal probability).

• Press the "Single Step" button to run a single time step.

• Press the "Start" button to run continuously. (The button then turns into a "Stop" button, which you can press to stop running.)

• You can select the running speed, from among Slow, Fast, and Fastest.

• The "Time step" label indicates how many time steps have been run (the counter is reset by certain operations).

• You can use the mouse to "draw" in the array in order to change the states of cells. The "Drawing state" item lets you specify which value the mouse will draw into the cells.

• The Drawing Brush Size lets you draw more than one cell at a time; you can draw an NxN box of cells (the mouse is at the upper-left corner of the "paint brush").

In addition, some rules have their own special controls, e.g. which let you change the number of states, or vary the neighborhood used, etc. See the individual applets' web pages for more information.