I also made a pretty graph:

where the points are expressed with the previous parameterization:

f(2.8104771698906146985) = 0 + (...)i

f(2.316910654383280043 -- minimum real part

f(2.2893404841466060077) = (...) +i

f(2.1025947819458660569) = 0 + (...)i

f(1.9681078867187501493) = (...) + 2i

f(1.927907601568660839 -- maximum imaginary part

f(1.8909946364512036029) = 1 + (...)i

f(1.8869709745663253961) = (...) + 2i

f(1.5600433372731975189) = 2 + (...)i

f(1.5064318596452087082) = (...) + i

f(1.4488307492834293737) -- maximum real part

f(1.3099015915373765040) = 2 + (...)i

from this graph you can almost see how the area is almost 4, because it takes up almost 4 full squares, then it has some over-hand outside of these 4 squares, and the overhang looks like it could fill up the remaining area...

Andrew Robbins

where the points are expressed with the previous parameterization:

f(2.8104771698906146985) = 0 + (...)i

f(2.316910654383280043 -- minimum real part

f(2.2893404841466060077) = (...) +i

f(2.1025947819458660569) = 0 + (...)i

f(1.9681078867187501493) = (...) + 2i

f(1.927907601568660839 -- maximum imaginary part

f(1.8909946364512036029) = 1 + (...)i

f(1.8869709745663253961) = (...) + 2i

f(1.5600433372731975189) = 2 + (...)i

f(1.5064318596452087082) = (...) + i

f(1.4488307492834293737) -- maximum real part

f(1.3099015915373765040) = 2 + (...)i

from this graph you can almost see how the area is almost 4, because it takes up almost 4 full squares, then it has some over-hand outside of these 4 squares, and the overhang looks like it could fill up the remaining area...

Andrew Robbins