Exercises 45–48 illustrate the connection between nonperiodic tilings of the line and the Fibonacci numbers and golden ratio of Chapter 19 (but these exercises do not require any information from that chapter). (Thanks for this idea to David J. Wright, Oklahoma State University.) The rabbit problem in Chapter 19 (Exercise 4, page 814) leads us directly into quasiperiodic patterns (and even to musical sequences, as later exercises show). Let (for “adult”) denote an adult pair of rabbits and (for “baby”) denote a baby pair. We record the population at the end of each month, just before any births, in a systematic way, as a string of s and s. At the end of their second month of life, a rabbit pair will be considered to be adult and give birth to a baby pair.

At the end of the first month, the sequence is just , and the same is true at the end of the second month. When an adult pair has a baby pair , we write the new immediately to the right of the . So at the end of the third month, the sequence is ; at the end of the fourth, it is because the first baby pair is now adult; at the end of the fifth month, we have . (In this model, rabbits breed like clockwork, month after month, and never die!)