Sensitivity To Peturbation in Elementary Cellular Automata

How does information travel in cellular automata? One way to investigate this is to compare computations whose initial conditions differ by only a single cell.

In this Demonstration, we run a cellular automaton in the left panel starting from a random initial condition. In the right panel, we run the same cellular automaton changing exactly one cell in the initial condition. That cell is colored purple, as are the ones in lower rows that change as a consequence.

We can see how the evolution responds to changes in the position of the initial changed cell.

Overall, we can see that different behaviors tend to channel information in different ways. Class 3 rules that generate intrinsic randomness allow the perturbation to spread everywhere. Class 4 rules spread information in complex and unpredictable ways, often along particular channels. In Class 1 and 2 rules, the information either dies out or travels in a repetitive, regular way.