Phyllotactic patterns and pattern quarks and leptons

植物上叶（叶、花、种子、苞片）的排列和它们的表面形态吸引和迷惑了科学家们400多年。一个特殊的挑战是理解为什么在许多植物上，比如向日葵，种子位于顺时针和逆时针螺旋的家族中，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，称为斐波那契数，它由任意两个整数开始，并将每个后续成员定义为前两个整数的和。谷歌向日葵图片，自己数数。你会遇到美丽的葵花籽头与21,34和55家族螺旋。数一数。我们可以生成这个最常见的斐波那契数列，从1,2开始，得到1,2,3,5,8,13,21,34,55... .解释层序结构的尝试分为两类。目的论的方法设计了定位下一粒种子或花朵的规则，以便以某种最佳方式包装种子，这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。这可能就是为什么有条纹的老虎比没有条纹的老虎更有进化优势的原因，但大自然必须使用简单而古老的物理和生化过程来实现这些结果。在植物中，叶根形成的机制涉及到导致生长素激素分布不均匀的不稳定性（叶根形成将发生在生长素场的最大值）和植物生长尖端附近不均匀的应力场。然后，相应的模式作为一个前沿繁殖，并为叶状芽形成创造潜在的位点。我们得到了一些令人震惊的新结果，这些结果表明，不稳定性产生的模式场的最大值的位置与目的论启发模型产生的点组态是一致的。这提出了一个令人兴奋的新想法，即在许多情况下，不稳定产生的模式可能是植物和其他生物追求最佳策略的机制。它也建议替代的方法来调查许多开放的挑战在最优包装。

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.