Data Analysis by Driven IFS

Exercise Answers

3. (a)

The bin transitions are 1 -> 2, 2 -> 3, 3 -> 4, and 4 -> 1.

Consequently, the only occupied length 2 addresses are 21, 32, 43 and $14.

The empty length 2 addresses are the remaining twelve: 11, 12, 13, 22, 23, 24, 31, 33, 34, 41, 42 and 44.

Note the allowed bin-to-bin transitions determine a cycle, 1 -> 2 -> 3 -> 4 -> 1.

From this we see the driven IFS converges to the 4-cycle consisting of the points having addresses (4321)infinity, (3214)infinity, (2143)infinity and (1432)infinity.

These bin transitions can be encoded in the transition graph

Return to Exercises.