At each stage the length of the curve
doubles so that at Stage n the length is 4×2n units. The area inside the curve is always 1 square unit and the length of the
curve is infinite as 2n ® ¥ as n ® ¥.
For 4×2n = 1000000 we have
n =
log (2.5×105)log 2
» 17.9.
Note that 217=131072 < 250000 but 218=262144 > 250000.
So at the 18th iteration the curve is longer than a million units.
The magnification factor is 4 and the generator contains 8 copies of
the line segment it replaces so the dimension is given by