For Exercises 52–62, refer to the following. Call a sequence musical if repeatedly applying deflation to it eventually results in a single .
62. (For students who have covered Chapter 19.) After applying deflation a large number of times, a large area of a Penrose pattern will contain some number kites and darts. At each deflation, a kite is broken down into two kites and two halves of darts, and a dart is broken down into a single kite and two halves of darts. Thus, each of the kites gives rise to 2 kites, and each of the darts gives rise to kites, for a total of new kites. Similarly, there will be new darts. The ratio of kites to darts will become
Assume that the ratio eventually stabilizes as the number of darts and kites gets larger and larger. What value does it tend to? Hint: Set and solve for .