This article is a review and at the same time contains a number of original ideas and results that allow to formulate the principal reason for the hexagon formation in systems of animate and inanimate nature. The main goal of this study lies in the application of synergetic methods at the border of physics and medicine. More precisely, a synergetic analogy is considered between two systems of absolutely different nature in which hexagonal structures arise, namely: (a) the physical system of Benard cells and (b) the neurophysiological system of grid cells in the brain (Nobel Prize in physiology or medicine in 2014, which was awarded to J.O'Keefe, E.I.Moser, and M.-B.Moser). To explain the principal reason of the hexagon formation in the brain, “Feynman's classification of three stages in studying natural phenomena” is proposed to use, especially the 3rd stage of studying, associated with the understanding first principles underlying these phenomena.

On the basis of the proposed fluctuation model, in which the Ginzburg-Landau Hamiltonian, the Polyakov hypothesis of conformal invariance, and Haken results on Benard cells are used, the first principle for the hexagon formation in system of grid cells is formulated as a manifestation of the nonlinear interaction of order-parameter fluctuations. The vertices of the virtual hexagon in 6-grid lattice represent the geometric place of those points at which the interaction of fluctuations is realized and the action potential (AP), i.e. a so-called “firing of AP”, appears in neurons. In accordance with the universality hypothesis and synergetic similarity of hexagon formation in systems of Benard and grid cells, these both systems should belong to the same universality class of the 3-dimensional Ising model having a scalar order parameter. This class of universality includes classic liquids and liquid mixtures, liquid crystals in the Maier-Saupe approxamation, chemically reacting system of grid cells in the brain and other systems. Another goal of the article is to attract the attention of researchers (not only physicists, chemists and mathematicians, but also neurophysiologists, biologists and physicians) to the problem of structure formation in living and inanimate world, using ideas of the fluctuation theory of phase transitions and critical phenomena, statistical thermodynamics, universality classes, scaling and conformal invariance hypotheses.

本文是一篇评论，同时包含了许多原始的思想和结果，这些思想和结果可以阐明有生命和无生命性质的系统中六边形形成的主要原因。这项研究的主要目标在于在物理和医学界应用协同方法。更确切地说，可以考虑在两个性质完全不同的六边形结构系统之间进行协同类比，即：（a）Benard细胞的物理系统和（b）大脑中网格细胞的神经生理系统（诺贝尔生理学奖）或2014年获得医学奖项，分别授予J.O'Keefe，EIMOser和M.-B.Moser。为解释大脑中六边形形成的主要原因，建议使用“费恩曼研究自然现象的三个阶段的分类”，

在提出的波动模型的基础上，使用了Ginzburg-Landau哈密顿量，保形不变的Polyakov假设以及Benard细胞的Haken结果，提出了网格单元系统中六边形形成的第一个原理作为体现。参数波动的非线性相互作用 6格网格中的虚拟六边形的顶点表示实现波动相互作用并且在神经元中出现动作电位（AP）（即所谓的“ AP点火”）的那些点的几何位置。根据Benard和网格单元系统中六角形形成的普遍性假设和协同相似性，这两个系统应属于具有标量阶数参数的3维Ising模型的相同普遍性类别。此类通用性包括经典的液体和液体混合物，Maier-Saupe近似中的液晶，大脑中网格细胞的化学反应系统以及其他系统。本文的另一个目标是利用相变的涨落理论，吸引研究人员（不仅是物理学家，化学家和数学家，而且是神经生理学家，生物学家和医师）关注生活和无生命世界中的结构形成问题。和临界现象，统计热力学，通用性分类，缩放和共形不变性假设。