The self-assembly of molecular and macromolecular building blocks into organized patterns is a complex process found in diverse systems over a wide range of size and time scales. The formation of star- or aster-like configurations, for example, is a common characteristic in solutions of polymers or other molecules containing multi-scaled, hierarchical assembly processes. This is a recurring phenomenon in numerous pattern-forming systems ranging from cellular constructs to solutions of ferromagnetic colloids or synthetic plastics. To date, however, it has not been possible to systematically parameterize structural properties of the constituent components in order to study their influence on assembled states. Here, we circumvent this limitation by using DNA nanotubes with programmable mechanical properties as our basic building blocks. A small set of DNA oligonucleotides can be chosen to hybridize into micron-length DNA nanotubes with a well-defined circumference and stiffness. The self-assembly of these nanotubes to hierarchically ordered structures is driven by depletion forces caused by the presence of polyethylene glycol. This trait allowed us to investigate self-assembly effects while maintaining a complete decoupling of density, self-association or bundling strength, and stiffness of the nanotubes. Our findings show diverse ranges of emerging structures including heterogeneous networks, aster-like structures, and densely bundled needle-like structures, which compare to configurations found in many other systems. These show a strong dependence not only on concentration and bundling strength, but also on the underlying mechanical properties of the nanotubes. Similar network architectures to those caused by depletion forces in the low-density regime are obtained when an alternative hybridization-based bundling mechanism is employed to induce self-assembly in an isotropic network of pre-formed DNA nanotubes. This emphasizes the universal effect inevitable attractive forces in crowded environments have on systems of self-assembling soft matter, which should be considered for macromolecular structures applied in crowded systems such as cells.