An activator-inhibitor reaction-diffusion system on a 1D cell membrane spontaneously breaks symmetry, establishing a polarized state. The activator (A) self-amplifies locally while the inhibitor (H) diffuses faster, creating a single concentration peak — the cell's "front".
Turing instability requires D_H ≫ D_A. The homogeneous steady state (A₀, H₀) becomes unstable to spatially heterogeneous perturbations when the inhibitor diffuses fast enough to suppress activator globally while the activator amplifies locally. For a cell, this spontaneously selects one end as the "front".