Fractal patterns in torn garbage bags, leaves, flowers, and water-oil interfaces

• Coloquios

Harry L. Swinney

University of Texas at Austin

Lunes 15/3/2010, 14 hs
Aula Federman, 1er piso, Pabellón I 

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 and the edges of leaves (e.g., some lettuce). By applying simple growth laws and principles from physics and geometry, it is possible to understand how a thin flat leaf, flower, or plastic sheet can spontaneously break symmetry and generate complex fractal patterns. Similar fractal patterns form also when water from the underground water table penetrates into an oil reservoir above it, as happens when oil is pumped from the ground. A consequence of this "viscous fingering" is that only about half of the oil can be removed from a reservoir. Viscous fingering patterns will be shown to exhibit precisely the same mathematical properties as a simple computer model that generates fractal structures.