\n<\/strong><\/p>\n
Venue \u00a0\u00a0 : Thu 15 Sept 2016, 3pm (Murdoch University, Senate Room)<\/strong><\/p>\n Phyllotaxis (the arrangement of buds or branches on a stem, or\u00a0 flowerets on a flower) has long been debated [1, 2], particularly in regard to the widespread occurrence of spiral structures that are related to the Fibonacci sequence [3-7]. Over the years hundreds of papers, and several books, have attempted to provide explanations of this phenomenon using models of varying complexity, sophistication and ad hoc inventiveness.<\/p>\n Here we off\u000ber a theoretical model which relates the problem to disk packings, extending previous work [8, 9] that seeks explanations in that way. Our method Buds are introduced at the top of a “bullet-shaped” surface – roughly representative of a plant stem, see Fig (1) – and migrate downwards, while conforming to three principles: dense packing, homogeneity and continuity. Typical results are presented in a video. We show that spiral structures characterised by the Fibonacci sequence (1,1,2,3,5,8,13…), as well as related structures, occur naturally under such rules.<\/p>\n A. M. acknowledges fi\fnancial support through Aberystwyth University Research Fund.<\/p>\n [1] H. Airy, Proceedings of the Royal Society of London 21, 176 (1872). Phyllotaxis, disk packing and Fibonacci numbers Speaker : Dr Adil Mughal – Aberystwyth University, Wales Venue \u00a0\u00a0 : Thu 15 Sept 2016, 3pm (Murdoch University, Senate Room) Phyllotaxis (the arrangement of buds or branches on a stem, or\u00a0 flowerets on a flower) has long been debated [1, 2], particularly in regard to the widespread occurrence […]<\/p>\n","protected":false},"author":1,"featured_media":1058,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-1059","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/from-snot-to-tissue-org.gerdschroeder-turk.org\/wp-content\/uploads\/2016\/06\/2016_09_15_AdilMughal.png?fit=1280%2C450&ssl=1","_links":{"self":[{"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/posts\/1059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1059"}],"version-history":[{"count":3,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/posts\/1059\/revisions"}],"predecessor-version":[{"id":1122,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/posts\/1059\/revisions\/1122"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=\/wp\/v2\/media\/1058"}],"wp:attachment":[{"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/from-snot-to-tissue-org.gerdschroeder-turk.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nis to adapt the closely related problem of the dense packing of hard disks on a cylinder [10{12], where helical symmetry arises naturally, to the present case of
\nbuds on a gradually enlarging stem.<\/p>\n![\"2016_09_15_AdilMughal2\"](\"https:\/\/i0.wp.com\/from-snot-to-tissue-org.gerdschroeder-turk.org\/wp-content\/uploads\/2016\/06\/2016_09_15_AdilMughal2.png?resize=447%2C186&ssl=1\")
\n[2] D. Hofstadter and C. Teuscher, Alan Turing: Life and legacy of a great thinker (Springer Science & Business Media, 2013).
\n[3] L. Levitov, JETP letters 54, 542 (1991).
\n[4] L. Levitov, EPL (Europhysics Letters) 14, 533 (1991).
\n[5] S. Douady and Y. Couder, Physical Review Letters 68, 2098 (1992).
\n[6] P. Atela, C. Gol\u0013e, and S. Hotton, Journal of Nonlinear Science 12, 641 (2002).
\n[7] M. Pennybacker and A.C. Newell, Physical Review Letters 110, 248104 (2013).
\n[8] G.J. Mitchison, Science (1977).
\n[9] G. Van Iterson, Mathematische und mikroskopisch-anatomische Studien uber Blattstellungen: nebst Betrachtungen \u00fcber den Schalenbau der Miliolinen, Ph.D. thesis, TU Delft, Delft University of Technology (1907).
\n[10] A. Mughal, H. Chan, and D. Weaire, Physical Review Letters 106, 115704 (2011).
\n[11] A. Mughal, H. Chan, D. Weaire, and S. Hutzler, Physical Review E 85, 051305 (2012).
\n[12] A. Mughal and D. Weaire, Physical Review E (2014).<\/p>\n","protected":false},"excerpt":{"rendered":"