Third Homework Set Answers

1(a) The few points in the interior of the square come from starting the driven IFS at (.5,.5).

To understand the other points, we divide the time series into regimes where the bin occupancy changes.

To the left of line 1 all data points lie in bins 1 and 2, so the driven IFS generates the line between corners 1 and 2.

Between lines 1 and 2, all data points line in bin 2, so the driven IFS points go to corner 2.

Between lines 2 and 3 all data points lie in bins 2 and 4, so the driven IFS generates the line between corners 2 and 4.

Between lines 3 and 4, all data points line in bin 4, so the driven IFS points go to corner 4.

Between lines 4 and 5 all data points lie in bins 3 and 4, so the driven IFS generates the line between corners 3 and 4.

Between lines 5 and 6, all data points line in bin 3, so the driven IFS points go to corner 3.

To the right of line 6 all data points lie in bins 1 and 3, so the driven IFS generates the line between corners 1 and 3.

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