TY - JOUR
T1 - Phyllotaxis, pushed pattern-forming fronts, and optimal packing
AU - Pennybacker, Matthew
AU - Newell, Alan C.
PY - 2013/6/13
Y1 - 2013/6/13
N2 - We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas, and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the advancing pushed pattern front chooses spiral families enumerated by Fibonacci sequences with all attendant self-similar properties, a new amplitude invariant curve, and connect the results with the optimal packing based algorithms previously used to explain phyllotaxis. Our results allow us to make experimentally testable predictions.
AB - We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas, and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the advancing pushed pattern front chooses spiral families enumerated by Fibonacci sequences with all attendant self-similar properties, a new amplitude invariant curve, and connect the results with the optimal packing based algorithms previously used to explain phyllotaxis. Our results allow us to make experimentally testable predictions.
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U2 - 10.1103/PhysRevLett.110.248104
DO - 10.1103/PhysRevLett.110.248104
M3 - Article
C2 - 25165965
AN - SCOPUS:84879107433
SN - 0031-9007
VL - 110
JO - Physical review letters
JF - Physical review letters
IS - 24
M1 - 248104
ER -