Say you have a filament that's 1 µm in diameter, and 1 meter long. You want to fill up a 1m^3 (1m W x 1m H x 1m L) space with these, how many of these can you place in such a space? Over a trillion! And thus, the combined km length of these will also be over a billion km. At such small scales things can become very long when summed up.
It is obvious when you think that 3d volumes scale cubicly and 1d lengths scale linearly. Adding another 1 meter to a cube of said filaments would increase the total length by a power of 3!
How would this compare with packing the volume with DNA ?
Everytime I see people talking about the length of their coastlines ...
Look at how long this edge of my fractal is, Ma!