Pattern Formation
Spatial patterns turn up all over the place, from whorls on your fingertips and hexagons gently frying in a pan to stripes on a zebra. Though many aspects of pattern formation are independent of the small details of the environment, often these natural systems or experiments are interesting in their own right. Ripples in sandy deserts and target patterns during the oxidation of carbon monoxide on platinum catalysts are examples that we have studied in depth.
Superlattice patterns are spatially periodic patterns that are periodic on a longer lengthscale than the more common patterns of stripes, squares and hexagons. Although superlattice patterns can exist in any physical system which has planar Euclidean symmetry, they have been seen in only relatively few experiments, such as the Faraday wave experiment. So what is it about this experiment which means that superlattice patterns, and their close relations, quasipatterns, can be stable? Recent theoretical work has established some of the pattern selection mechanisms at play, but there are still many open questions.
