The human brain exhibits a diverse yet constrained range of activity states. While these states can be faithfully represented in a low-dimensional latent space, our understanding of the constitutive functional anatomy is still evolving. Here we applied dimensionality reduction to task-free and task fMRI data to address whether latent dimensions reflect intrinsic systems and if so, how these systems may interact to generate different activity states. We find that each dimension represents a dynamic activity gradient, including a primary unipolar sensory-association gradient underlying the global signal. The gradients appear stable across individuals and cognitive states, while recapitulating key functional connectivity properties including anticorrelation, modularity, and regional hubness. We then use dynamical systems modeling to show that gradients causally interact via state-specific coupling parameters to create distinct brain activity patterns. Together, these findings indicate that a set of dynamic, intrinsic spatial gradients interact to determine the repertoire of possible brain activity states.