This book is about patterns: stripes on tigers, whorls in your fingerprints, ripples in sandy deserts, and hexagons you can cook in your own kitchen. More precisely it will be concerned with fairly regular spatial or spatiotemporal patterns that are seen in natural systems – deserts, fingertips, animal coats, stars – and in laboratory or kitchen experiments. These are structures you can pick out by eye as being special in some way, typically periodic in space (Figure 1.1), at least locally. The most common are stripes, squares and hexagons – periodic patterns that tesselate the plane – and rotating spirals or pulsating targets. Quasipatterns with twelvefold rotational symmetry (Figure 1.2) never repeat in any direction, but they look regular at a casual glance, while spiral defect chaos (Figure 1.3) is disordered on a large scale, but locally its constituent moving spirals and patches of stripes are spatially periodic.

Similar patterns are seen in wildly different natural contexts: for example, zebra stripes, desert sand ripples, granular segregation patterns and convection rolls all look stripy, and they even share the same dislocation defects, where two stripes merge into one (Figure 1.4). Rotating spirals appear in a dish of reacting chemicals and in an arrhythmic human heart. Squares crop up in convection and in a layer of vibrated sand. It turns out to be common for a given pattern to show up in several different systems, and for many aspects of its behaviour to be independent of the small details of its environment.