Third Homework Set Answers

1(d) Note the time series breaks into six distinct regimes, indicated by the vertical lines.

Left regime: points lie in bins 1, 2, and 3, not in 4. The IFS driven by this portion of the time series lies on the Sierpinski gasket with vertices (0,0), (1,0), and (0,1).

Next regime: points lie in bins 1 and 2. The IFS driven by this portion of the time series lies on the horizontal line with vertices (0,0) and (1,0).

Next regime: points lie in bin 2. The IFS driven by this portion of the IFS converges to the point (1,0).

Next regime: points lie in bins 2 and 4. The IFS driven by this portion of the time series lies on the vertical line with vertices (1,0) and (1,1).

Next regime: points lie in bin 4. The IFS driven by this portion of the IFS converges to the point (1,1).

Next regime: points lie in bins 1 and 4. The IFS driven by this portion of the time series lies on the diagonal line with vertices (0,0) and (1,1).

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