Single-wall carbon nanotubes are attractive building blocks for various devices, though the ability to arrange them into complex structures is a vital prerequisite for realizing their full potential. Our group has shown that by combining gas flow alignment and the anisotropy of the nanotube-substrate interaction, highly periodic ordered nanotube serpentines are formed. In this work we demonstrate the formation of a different type of nanotube serpentines by isotropic substrate interaction. By comparing the geometric properties and correlation lengths of the two types of serpentines, we show that these nanotube serpentines are markedly random and disordered, in comparison with the ordered serpentines. This also allows us to investigate the role of substrate anisotropy on the formation of nanotube serpentines. We also propose a general mechanism for the formation of self-organized curved nanotube geometries, such as serpentines and loops, on substrates.