# Exercises for Chaos Under Control

## Chapter 9: Cellular Automata

1. What happens to the initial configuration under the rule ? Answer

2. Determine by hand the first six generations of the starting configuration using the rule .Answer

3. Determine by hand the first six generations of the starting configuration using the rule or .Answer

4. Suppose we select the rule . What would happen to the completely off starting configuration in successive generations? Answer

5.[C] Use 1DIM to test the rule for a random starting configuration.

Exercises 6-8 use the rule or .

6. Determine by hand the first six generations of the starting configuration . Answer

7.[C] Use 1DIM to investigate the long-term behavior in exercises 3 and 6.

8.[C] Use 1DIM to investigate how the pattern changes as the two initial live cells are moved farther and farther apart. Can you discern any pattern?

9. Determine by hand the first six generations of the starting configuration using the rule or . Answer

10. Determine by hand the first six generations of the starting configuration using the rule or . Answer

11.[C] Use 1DIM to investigate the long-term behavior in exercises 9 and 10.

12. Determine by hand the first six generations of an initial single on-cell for the von Neumann automaton with the following rule: a dead central cell becomes alive in the next generation if exactly one of its four neighbors (N, S, E, or W) is alive in the current generation. Answer

13. Determine by hand the first six generations of an initial single on-cell for the Moore automaton with the following rule: a dead central cell becomes alive in the next generation if exactly one of its eight neighbors is alive in the current generation. Answer

14.[C] Explore some 3-cell and some 5-cell neighborhood automata with 1DIM. Try Central, Random, and various HomeMade seeds. Keep track of the kinds of patterns you see. After you run a particular rule with a Central seed, try to predict the result when you run the same rule with a HomeMade seed consisting of two on-cells. Does the result depend on how far apart the on-cells are?