Third Homework Set Answers

1(f) Note the time series breaks into five 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 bins 1, 2, and 4, but not in bin 3. The IFS driven by this portion of the time series lies on a Sierpinski gasket with vertices (0,0), (1,0), and (1,1).

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

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

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