Data Analysis by Driven IFS

Exercise Answers

3. (b)

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

Consequently, the only occupied length 2 addresses are 41, 24, 32 and 13.

The empty length 2 addresses are the remaining twelve: 11, 12, 14, 21, 22, 23, 31, 33, 34, 42, 43 and 44.

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

From this we see the driven IFS converges to the 4-cycle consisting of the points having addresses (3241)infinity, (2413)infinity, (4132)infinity, and (1324)infinity.

These bin transitions can be encoded in the transition graph

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