The Guided Pattern

Active fluids form patterns on their own. An inhomogeneous environment can guide which patterns form.

Active stresses in biological cells drive flow, deformation, and self-organization. In a uniform environment, the patterns that emerge — contractile foci, extensile flows, asters, spirals — are selected by the internal activity and the material’s elastic properties. The environment is passive: it provides boundary conditions but doesn’t participate in pattern selection.

Bächer, Schrader, and Mazza (arXiv:2603.07367) show that an inhomogeneous environment changes this picture fundamentally. When the material surrounding the active fluid has spatially varying properties — stiffness, viscosity, confinement — the environment becomes an active participant in pattern formation. It doesn’t just modify the patterns; it selects them.

The minimal model couples an active gel (with contractile or extensile stress) to a passive elastic medium with spatially varying elastic modulus. Where the environment is stiff, the active material is constrained and patterns are suppressed. Where it’s soft, patterns grow freely. The boundary between stiff and soft regions acts as an organizing center: patterns nucleate there and spread into the soft domain.

The key result is that the environment can guide patterns that would not form in its absence. A spatially varying stiffness can break a symmetry that the active material alone would preserve, selecting a specific pattern from a degenerate set. The pattern reflects the environment’s heterogeneity, not just the active fluid’s intrinsic dynamics.

In development, this matters: the extracellular matrix isn’t uniform. Its spatial heterogeneity guides the patterns that active cellular flows produce, acting as a template that the biology reads through mechanics.

Bächer, Schrader, and Mazza, “Active Fluid Patterning in Inhomogeneous Environments,” arXiv:2603.07367 (2026).