Phyllotactic patterns and pattern quarks and leptons

叶序图案和图案夸克和轻子

• 批准号: 1308862
• 负责人: Alan Newell
• 金额: $ 24.52万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1308862&HistoricalAwards=false
• 关键词: Phyllotactic; patterns; pattern; quarks; leptons

The arrangements of phylla (leaves, flowers, seeds, bracts) on plants and their surface morphologies have intrigued and mystified scientists for over four hundred years. A special challenge has been to understand why on many plants such as the sunflower, the seeds lie on families of clockwise and counterclockwise spirals and that the numbers in each family belong not just to the integers but to a special subset known as Fibonacci numbers generated by starting with any two integers and defining each successive member as the sum of the previous two. Google sunflower images and count for yourselves. You will encounter beautiful sunflower seed heads with 21, 34 and 55 family spirals. Count them. One can generate this, the most common, Fibonacci sequence by beginning with 1,2 and obtain 1,2,3,5,8,13,21,34,55... .Attempts to explain phyllotactic configurations fall into two categories. The teleological approach devises rules for positioning the next seed or flower so as to pack the seeds in some optimal fashion and is philosophically equivalent to saying the reason tigers have stripes is that it provides better camouflage. Now that may be the reason that striped tigers had an evolutionary advantage over unstriped ones, but nature has to use plain old physical and biochemical processes to achieve these outcomes. In plants, the mechanisms by which phylla are made involve instabilities which lead to a non uniform distribution of the hormone auxin (phylla initiation would occur at maxima of the auxin field) and non uniform stress fields in the vicinity of the plant's growth tips. The corresponding pattern then propagates as a front and creates potential sites for phylla initiation. What we have obtained is some stunning new results which demonstrate that the locations of the maxima of the instability generated pattern fields coincide with the point configurations generated by the teleologically inspired models. This suggests the exciting new idea that in many circumstances nstability generated patterns may be the mechanisms by which plants and other organisms can pursue optimal strategies. It also suggests alternative approaches to investigate many of the open challenges in optimal packing.

植物的叶（叶、花、种子、苞片）的排列及其表面形态已经吸引了科学家四百多年。一个特殊的挑战是理解为什么在向日葵等许多植物上，种子位于顺时针和逆时针螺旋家族中，并且每个家族中的数字不仅属于整数，而且属于一个称为斐波那契数的特殊子集，该子集是通过从任意两个整数开始并将每个连续成员定义为前两个的和而生成的。谷歌向日葵图片和计数为自己。你会遇到美丽的向日葵种子头与21，34和55家庭螺旋。数数我们可以从1，2开始生成这个最常见的斐波那契数列，并得到1，2，3，5，8，13，21，34，55. 试图解释叶序构型的尝试分为两类。目的论的方法设计了放置下一粒种子或花的规则，以便以某种最佳方式包装种子，在理论上相当于说老虎有条纹的原因是它提供了更好的伪装。这可能就是为什么条纹虎比无条纹虎具有进化优势的原因，但大自然必须使用普通的物理和生物化学过程来实现这些结果。在植物中，形成叶的机制涉及不稳定性，其导致激素生长素的不均匀分布（叶起始将发生在生长素场的最大值处）和植物生长尖端附近的不均匀应力场。相应的模式，然后传播作为一个前线，并创造潜在的网站叶开始。我们所得到的是一些令人惊叹的新结果，这些结果表明，不稳定性产生的图案场的最大值的位置与目的论启发的模型产生的点配置相一致。这提出了一个令人兴奋的新想法，即在许多情况下，不稳定性产生的模式可能是植物和其他生物体追求最佳策略的机制。它还提出了其他方法来研究最佳包装中的许多开放挑战。