The figure shows the steps to producing a curve .
It starts as the boundary of the unit square in Figure (a).
In Figure (b),
we remove a square quarter of the area of the square in (a).
In Figure (c), we add a square quarter of the area that we removed in (b).
In Figure (d),
we remove a square quarter of the area of the square we added in (c).
If we continue to do this indefinitely, we will get the curve .
We let be the region enclosed by .
By summing a suitable infinite series,
find the area of region . Give your answer as a fraction.