A New Fast Method for Determining Local Properties of Striped Patterns

Abstract

From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide variety of fields have been studying the patterns formed in well-controlled experiments that yield enormous quantities of high-precision data. These experiments involving phenomena as diverse as chemical reactions in shallow layers, thermal convection in horizontal fluid layers, periodically shaken layers of sand, and the growth of slime mold colonies often display patterns that appear qualitatively similar. Methods are needed to characterize in a reasonable amount of time the differences and similarities in patterns that develop in different systems, as well as in patterns formed in one system for different experimental conditions. In this Letter, we introduce a novel, fast method for determining local pattern properties such as wavenumber, orientation, and curvature as a function of position for locally striped patterns.