in this talk, i will explore the interesting geometries that emerge in high-dimensional attraction basins, which are important in applications such as protein folding, cell differentiation, and neural networks. as a paradigmatic model, i will consider networks of coupled kuramoto oscillators and show that high-dimensional basins generally cannot be approximated by simple convex shapes. instead, they have tentacle-like structures where most of the basin volume is concentrated. next, i will show that introducing non-pairwise couplings among kuramoto oscillators can make basins deeper but smaller—the attractors become linearly more stable but much harder to find due to basins shrinking dramatically. time allowing, i will also briefly mention a few related projects, including learning basins with reservoir computing and modeling circadian clocks with kuramoto oscillators.