A variety of pattern formation phenomena in catalytic surface reactions can be attributed to the dynamics of interfaces, or fronts, separating distinct uniform states. The states may represent surface coverages by different adsorbates or in the case of forced oscillations, different phases of oscillation. The dynamics of fronts are strongly affected by front instabilities and by diffusion anisotropy. We identify two new pattern formation mechanisms associated with different front behaviors in orthogonal directions: an ordering process by which stationary labyrinths in an isotropic system evolve into ordered stationary stripes, and confinement of isotropic spatiotemporal chaos to one space dimension, a state we term stratified chaos.