TY - JOUR
T1 - Phyllotaxis, disk packing, and Fibonacci numbers
AU - Mughal, Adil
AU - Weaire, Denis
N1 - This is the author accepted manuscript. The final version is available from American Physical Society via http://dx.doi.org/10.1103/PhysRevE.95.022401
PY - 2017/2/6
Y1 - 2017/2/6
N2 - We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity, and continuity. We show that spiral structures characterized by the widely observed Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...), as well as related structures, occur naturally under such rules. Typical results are presented in an animation
AB - We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity, and continuity. We show that spiral structures characterized by the widely observed Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...), as well as related structures, occur naturally under such rules. Typical results are presented in an animation
UR - https://arxiv.org/pdf/1608.05824
UR - http://hdl.handle.net/2160/44969
U2 - 10.1103/PhysRevE.95.022401
DO - 10.1103/PhysRevE.95.022401
M3 - Article
C2 - 28297965
SN - 1539-3755
VL - 95
JO - Physical Review E
JF - Physical Review E
IS - 2
M1 - 022401
ER -
