Pub Date : 2023-01-01DOI: 10.55060/j.gandf.230912.001
Edoardo De Tommasi, Alessandra Rogato
The link between shape and function allows understanding the evolutionary success of several organisms and their constituent parts. This is true in particular for diatoms, unicellular microalgae which contribute massively to primary production and carbon sequestration on a global scale, and which are characterized by an impressive diversity in dimension and shape within about 10 3 genera and up to 10 5 estimated species. The peculiar feature of diatoms is the frustule, a porous silica shell which encloses the protoplasm and which is characterized by the presence of regular patterns of micro-and nano-pores in an ultra-structured architecture. The diatom frustule seems to be involved in mechanical protection of the cell, sorting of nutrients from noxious agents, gas exchange, and efficient coupling with solar radiation. The aim of this short review is to give on one hand an overview of the main genetic mechanisms which finely control frustule morphogenesis and, on the other hand, to focus on its photonic properties, which could contribute to understand the extraordinary efficiency of diatoms in photosynthesis. The discussion on frustule morphogenesis and optical functions has been linked to Gielis transformations as an elegant and efficient tool to describe its geometry.
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Pub Date : 1900-01-01DOI: 10.55060/j.gandf.220605.001
G. Dattoli, E. Di Palma, E. Sabia
The theory of dimensions in physics is astonishingly rich. It can be viewed at different levels of abstraction and, at any of these levels, reveals deep suggestions. The relevant theory was initially developed to get a useful mean to reduce the number of variables in experiments. Within this context Rayleigh method and Buckingham Π theorem are highly conceptual working tools. Further elements of novelty have emerged during the last years and methods, directly or indirectly, linked to dimensional analysis, have become a central issue to treat families of differential equations, to enter deeply in the so-called scaling relations characterizing the phenomenology, not only in physics but in social science, economy, biology, and so on. This article is an effort aimed at providing a reasonably comprehensive account of the theory and the relevant practical outcomes, which spans over a large variety of topics including classical issues in hydrodynamics but also in general relativity and quantum mechanics as well.
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Pub Date : 1900-01-01DOI: 10.55060/j.gandf.220817.001
J. Gielis, P. Shi, D. Caratelli
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) a direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections.
{"title":"Universal Equations – A Fresh Perspective","authors":"J. Gielis, P. Shi, D. Caratelli","doi":"10.55060/j.gandf.220817.001","DOIUrl":"https://doi.org/10.55060/j.gandf.220817.001","url":null,"abstract":"A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) a direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections.","PeriodicalId":428727,"journal":{"name":"Growth and Form","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123312372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.55060/j.gandf.230712.001
M. He
It is well known that a genetics system in biology delivers the biological organism’s self-reproduction in their generations. Similarly, the “golden ratio” in mathematics keeps its self-reproduction property in their iterations. The biological system divides the genetic four-letter alphabet (A, C, G, T/U) into various three pairs of letters. There are three kinds of genetic equivalences among these four-letter alphabets (A=C, G=U; A=G, C=U; A=U, C=G). In this paper, we investigate the geometric shapes and forms associated with these three kinds of genetic code equivalences. We show that each equivalence has its own geometric shape and form. These geometric properties include attracting fixed point, repelling fixed point, basin of attractions, Julia sets and corresponding Mandelbrot sets. We further study the golden ratio, ring ratio and unity ratio matrices associated with three kinds of genetic code equivalences.
众所周知，生物学中的遗传系统使生物有机体的自我繁殖代代相传。同样，数学中的“黄金比例”在它们的迭代中保持着自我复制的特性。生物系统将遗传的四字母字母表(A、C、G、T/U)分成不同的三对字母。这四个字母之间存在三种遗传等价(A=C, G=U;= G、C = U;= U, C = G)。本文研究了这三种遗传密码等价的几何形状和形式。我们证明每个等价都有它自己的几何形状和形式。这些几何性质包括吸引不动点、排斥不动点、吸引池、Julia集和相应的Mandelbrot集。进一步研究了三种遗传密码等价的黄金比例矩阵、环比例矩阵和单位比例矩阵。
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Pub Date : 1900-01-01DOI: 10.55060/j.gandf.221226.001
J. Gielis
In 2022, Growth and Form transitioned to Athena International Publishing. This was an important step to allow the journal to grow in the years to come. The basic idea is still to offer a variety of different perspectives on the natural sciences. The name of the journal comes from one of the most important natural science books of the 20th century, On Growth and Form by D’Arcy Wentworth Thompson [1], which combined a wide range of models from applied mathematics and physics with biological phenomena and growth. D’Arcy Thompson’s central message is: “The living and the dead, things animate and inanimate, we dwellers in the world and this world wherein we dwell – πάντα γα μὰν τὰ γιγνωσκόμενα1 – are bound alike by physical and mathematical law.”
2022年，《成长与形态》由雅典娜国际出版公司出版。这是一个重要的步骤，使该杂志在未来几年的发展。其基本思想仍然是提供关于自然科学的各种不同的观点。该杂志的名称来自20世纪最重要的自然科学书籍之一，D 'Arcy Wentworth Thompson的《On Growth and Form》[1]，该书将应用数学和物理学的广泛模型与生物现象和生长相结合。达西·汤普森的中心思想是:“生者与死者，有生命之物与无生命之物，我们居住在这个世界和我们居住的这个世界上——π α ντ ν γιγνωσκ ο μενα1——都受到物理和数学定律的约束。”
{"title":"Growth and Form – Volume 3","authors":"J. Gielis","doi":"10.55060/j.gandf.221226.001","DOIUrl":"https://doi.org/10.55060/j.gandf.221226.001","url":null,"abstract":"In 2022, Growth and Form transitioned to Athena International Publishing. This was an important step to allow the journal to grow in the years to come. The basic idea is still to offer a variety of different perspectives on the natural sciences. The name of the journal comes from one of the most important natural science books of the 20th century, On Growth and Form by D’Arcy Wentworth Thompson [1], which combined a wide range of models from applied mathematics and physics with biological phenomena and growth. D’Arcy Thompson’s central message is: “The living and the dead, things animate and inanimate, we dwellers in the world and this world wherein we dwell – πάντα γα μὰν τὰ γιγνωσκόμενα1 – are bound alike by physical and mathematical law.”","PeriodicalId":428727,"journal":{"name":"Growth and Form","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124888773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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