Data Analysis by Driven IFS

Exercise Answers

5. Here is the Driven IFS.

Note the data fall into three clearly different regimes, indicated by the vertical lines superimposed on the data plot.

In the first regime, the data fall into only bins 2, 3, and 4.

As we saw in exercise 4 (b), in the driven IFS this generates points lying on the gasket with vertices (1, 0), (0, 1) and (1, 1). We see this in the driven IFS plot.

In the second regime, all the data points fall into bin 2.

The driven IFS points march down to the point (1, 0).

In the third regime, the data fall into only bins 1 and 2.

Starting from (very near to) the point (1, 0), all combinations of T1 and T2 will fill the line between (0, 0) and (1, 0), so we expect to see many points along the bottom of the square. We see this in the driven IFS plot.

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