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HOME > PAST ISSUE > May-June 2004 > Article Detail

FEATURE ARTICLE

Leaves, Flowers and Garbage Bags: Making Waves

Rippled fractal patterns on thin plastic sheets and biological membranes offer elegant examples of the spontaneous breaking of symmetry

Eran Sharon, Michael Marder, Harry Swinney

 

Figure 4. Buckling cascadesClick to Enlarge Image

Biology is full of stunningly complex patterns that arise from the breaking of spatial symmetries. Sharon, Marder and Swinney have succeeded in understanding one type of pattern: the ripples that form at the edges of leaves and cylindrical flower parts, such as the trumpets of daffodils. These ripples can have fractal dimensions and look just like the ripples that form at the edges of a torn sheet of plastic. There's a reason for the similarity: The waves emerge from the geometrical properties of thin membranes, including biological ones. These membranes must buckle and break free of their Euclidean geometry. The authors explain how rippled edges form as a response to the stresses on a membrane as a plant grows, and how the expression of a growth hormone may control this phenomenon in plant leaves.


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