# 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?

Return to Chapter 9 Exercises

Go to Chapter 9 exercises: Outer Totalistic Rules

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