Abstract Rapid growth and extensive tissue infiltration are characteristics of highly malignant neuroepithelial brain tumors. Very little is known, however, about the existence of structure–function relationships in these types of neoplasm. Therefore, using a previously developed two-dimensional agent-based model, we have investigated the emergent patterns of multiple tumor cells that proliferate and migrate on an adaptive grid lattice, driven by a local-search mechanism and guided by the presence of distinct environmental conditions. Numerical results indicate a strong correlation between the fractal dimensions of the tumor surface and the average velocity of the tumor's spatial expansion. In particular, when the so called ‘beaten-path advantage’ intensifies, i.e., rising ‘mechanical rewards’ for cells to follow each other along preformed pathways, it results in an increase of the tumor system's fractal dimensions leading to a concomitant acceleration of its spatial expansion. Whereas cell migration is the dominant phenotype responsible for the more extensive branching patterns exhibiting higher fractal dimensions, cell proliferation appears to become more active primarily at lower fracticality associated with stronger mechanical confinements. Implications of these results for experimental and clinical cancer research are discussed.