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SUMMARY:Do we understand Fibonacci numbers in plants? - Dr Jonathan Swinto
n (Swinton.Net)
DTSTART;VALUE=DATE-TIME:20220304T140000Z
DTEND;VALUE=DATE-TIME:20220304T150000Z
UID:https://talks.ox.ac.uk/talks/id/9d4bc3e7-4eb8-43dd-8589-c63a315d1ae7/
DESCRIPTION:Fibonacci numbers in plants\, such as in sunflower spiral coun
ts\, have long fascinated mathematicians. For the last thirty years\, most
analyses have been variants of a Standard Model in which plant organs are
treated as point nodes successively placed on a cylinder according to a g
iven function of the previous node positions\, not too close or too far aw
ay from the existing nodes. These models usually lead to lattice solutions
. As a parameter of the model\, like the diameter of the cylinder\, is cha
nged\, the lattice can transition to another\, more complex lattice\, with
a different spiral count. It can typically be proved that these transitio
ns move lattice counts to higher Fibonacci numbers. While mathematically c
ompelling\, empirical validation of this Standard Model is as yet weak\, e
ven though the underlying molecular mechanisms are increasingly well chara
cterised. \n\nIn this talk I'll show a gallery of Fibonacci patterning and
give a brief history of mathematical approaches\, including a partially s
uccessful attempt by Alan Turing. I'll describe how the classification of
lattices on cylinders connects both to a representation of $SL(2\,Z)$ and
to applications through defining the constraint that any model must satisf
y to show Fibonacci structure. I'll discuss a range of such models\, how t
hey might be used to make testable predictions\, and why this matters.\n\n
From 2011 to 2017 Jonathan Swinton was a visiting professor to MPLS in Ox
ford in Computational Systems Biology. His new textbook Mathematical Phyll
otaxis will be published soon\, and his Alan Turing's Manchester will be
republished by The History Press in May 2022. \n\nSpeakers:\nDr Jonathan S
winton (Swinton.Net)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/9d4bc3e7-4eb8-43dd-8589-c63a315d1ae7/
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DESCRIPTION:Talk:Do we understand Fibonacci numbers in plants? - Dr Jonath
an Swinton (Swinton.Net)
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