Phyllotactic patterns and pattern quarks and leptons

四百多年来，植物门(叶、花、种子、苞片)在植物上的排列及其表面形态一直令科学家们感兴趣和困惑。一个特别的挑战是理解为什么在许多植物上，如向日葵，种子位于顺时针和逆时针螺旋的家族上，并且每个家族中的数字不仅属于整数，而且属于一个特殊的子集，称为斐波纳契数，通过从任何两个整数开始，并将每个连续的成员定义为前两个整数的总和。在谷歌上搜索向日葵图片，为自己算账吧。你会遇到美丽的葵花籽头，有21个、34个和55个家庭螺旋。数一数。人们可以通过从1，2开始生成这个最常见的斐波纳契数列，并得到1，2，3，5，8，13，21，34，55…解释语系结构的尝试分为两类。目的论方法设计了定位下一颗种子或花朵的规则，以便以某种最佳方式包装种子，在哲学上相当于说，老虎有条纹的原因是它提供了更好的伪装。这可能是条纹老虎比非条纹老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化过程来实现这些结果。在植物中，门的形成机制包括不稳定导致激素生长素的不均匀分布(门的起始发生在生长素场的最大值)和植物生长尖端附近的不均匀应力场。然后，相应的模式作为锋面传播，并为门的启动创造潜在的地点。我们所得到的是一些令人震惊的新结果，它们证明了不稳定性产生的图案场的极大值的位置与由目的论启发的模型产生的点的位形一致。这表明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有机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。

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.