Voronoi patterns

A Mathematical Approach to Understanding Volvox

Abstract This paper sheds light on the suitability of mathematical theories and models to unveil a variety of design solutions inherent to Volvox. Having evolved from the unicellular Chlamydomonas, Volvox demonstrates that multicellularity is of particular interest to improve the nutrient uptake per somatic cell. Also, randomness plays a role

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Art in Symmetry: Mathematical Models that Dictate Radiolarian Structures

– ABSTRACT – This essay explores the fascinating intersection of mathematics and biology through the study of Radiolaria, which are intricate marine protozoa known for their symmetrical skeletal structures. The idea of symmetry is the core of this investigation, highlighting how radial and bilateral formations in Radiolaria are not only

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Geometry is Key: Mathematical Modeling of Whiskers and Antennae

Abstract Rat whiskers can be  modeled by Euler spirals,  curves with linear change in curvature. One hypothesis explaining vibrissae shape is that the linear growth of rat whiskers creates linear curvature. Another hypothesis is that the Euler spiral is an optimal shape to satisfy its sensory needs. The patterning of…

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The Complexity of Spines and their Mathematical Connections

Physical phenomena seen in nature are often optimized and refined to achieve a particular function. Evaluating spines’ physical and chemical characteristics can only reveal so much in the story of the optimization process. Modeling is an extremely powerful tool to unlock the secrets of developing the hidden strengths of particular…

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A Geometrical Analysis of Different Animals’ Carapace

This article explores the applications of geometry to the carapace of different organisms. The initial focus is on the three-dimensional shape of the turtle carapace to introduce the Gomboc shape which provides the self-righting feature to the turtle based on its unique property of equilibrium points. Then, the patterns of…

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The Life Cycle of the Whiskers and Antennae of Animals and Insects 

This article explores the various chemical, cellular, and molecular mechanisms relevant to the life cycle of whiskers (barbels) and antennae. The growth of zebrafish barbel is characterized by elongation, vasculature development, and innervation of taste buds. Catfish barbels perform chemical and mechanical sensing; namely, their hyper-sensitive gustatory system enables catfish…

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