4. Cellular Automata and Fractal Evolution

Sensitivity to Initial Conditions

To illistrate the sensitivity to initial conditions of some CA, for each of four one-dimensional, N = 5 binary CA we show the patterns evolving from three initial conditions:
*   a single live cell,
*   two adjacent live cells, and
*   three adjacent live cells.
As you go through the examples, can you find a pattern?
one live cell
two live cells
three live cells
one live cell
two live cells
three live cells
one live cell
two live cells
three live cells
one live cell
two live cells
three live cells
Why do gaskets come up so frequently?
Random initial conditions also illustrate sensitivity in another way.
After some intital transient behavior, a persistent pattern may arise.
We might expect that a CA with this property would have only one persistent pattern.
This example shows that is not always true.
Click the small picture for a larger version. Click each large picture to remove it.

Return to Examples of Cellular Automata Patterns.