Third Homework Set Answers

1(b) Note the time series breaks into four 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).

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

Right central regime: points lie in bin 4. The IFS driven by this portion of the time series converges through the previous gasket to the point (1,1).

Right regime: points lie in bins 1 and 4. The IFS generated by this portion of the time series lies along the segment joining the points (1,1) and (0,0).

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