The emergence of patterns is one of the world’s most durable mysteries. Some patterns—clouds, snowflakes—form in space. Others—the ebb and flow of tides, seasonal wet and dry spells—are patterns that form in time. Natural patterns are mysterious because they are complex, organized and interconnected, even though the laws of physics on which they rest—Newton's classical laws of motion—are simple.
Figure 1. Nature’s geometries include wavy edges that sometimes assume the complex shapes called fractals, where a pattern repeats on different scales. One family of such patterns includes the complex wavy structures that are found along the edges of thin living tissues. The origin of this complexity turns out to be one of the more tractable problems in biological pattern formation. By applying simple growth laws and principles from physics and geometry and testing their ideas with flexible synthetic membranes, the authors have found that a leaf or flower—just like a torn sheet of plastic—can use an enhanced, uniform growth at its margins to generate such complex patterns. Examples of wavy edges in nature include some lichens (shown at top left, Sticta limbata), orchids (shown at top right, Schomborgkia beysiana), sea slugs (represented, bottom left, by Glossodoris hikuerensis) and ornamental cabbage.
Lichen photograph courtesy of Stephen Sharnoff; orchid photograph by Kjell Sandved/PhotoResearchers, Inc.; sea slug photograph courtesy of Jeff Jeffords; ornamental cabbage photograph by Yva Momatiuk and John Eastcott/PhotoResearchers,
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