Many studies that focus on physical systems make the simplifying assumption that direction is unimportant. Such systems are called isotropic. Water waves, for example, travel at the same speed in every direction, provided the depth of the water is fairly uniform. In the real world, many phenomena are highly dependent on direction. For example, velvet looks and feels differently when rubbed from different directions. Systems that are directionally dependent are called anisotropic.
The anisotropic image below was created using numerical simulations of wave patterns. When a wave is launched in all directions from the center of this anisotropic square, it creates this pattern after colliding with the edges of the anisotropic region.
Models of anisotropic materials are useful for understanding phenomena like the coordinated motions of tissues in a beating heart or the patterns that can form when chemicals flow through systems at rates that are directionally dependent."Complex-anisotropy-induced pattern formation in bistable media," Phys. Rev. E 79, 026105 (2009)