Patterns

Mathematical Models of Diatoms: Understanding Their Complex Shape, Reproduction and Chain Formation

Apart from physical and chemical solutions used by the diatom for survival, some features of the unicellular microalgae also could be described in mathematics. For instance, the diatom morphology reveals a striking alignment with the golden ratio and fractal geometry. By examining the silica shells of these unicellular algae, we…

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Proboscis Geometry, Allometry and the Mathematical Beauty of Spirals in Nature

Abstract The proboscis has many functions, notably feeding and mating, making it an incredibly useful organ. This paper aims to explore its structure and study the type of relationship between its components, called an allometric relationship. Allometry also appears when studying  how changes in structure affect some functions of the…

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Using Mathematical Principles to Gain a Deeper Understanding of the Form and Function of Hooves

The role of ungulates’ hooves, which are morphologically complex structures, is to support body weight and provide traction to aid in their adaptation to varied external conditions. This essay aims to investigate the relationship between the mathematical model and the morphology of the hoof. The golden ratio, an irrational constant…

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An Evolutionary Analysis of the Chemical Composition of Marine Suction Cups

Abstract Suction cups are important adaptations for aquatic animals, allowing for predation, locomotion, stability, and other species-specific functions. The chemical structure of each suction cup is designed by nature to be as energetically efficient as possible in performing the suction cup’s species-specific purpose, giving the suction cup chemical properties that…

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A Mathematical Analysis of Animal Horns

The following essay examines the application of mathematics to biological structures, in particular animal horns. It begins by exploring the evolutionary reasons for ornamental appendages among horned animals.  Mathematical computations reveal a relationship between ornament size and “honest advertisement” due to a high cost of having such large appendages. Furthermore,…

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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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Exploration of Mathematical Laws Governing Claws and their Applications within Flying Animals, Terrestrial Pests, and Amniotes

Claws are one of the most widely utilized tools within organisms, and for a good reason: their purposeful constructions, described by mathematical laws and correlations, allow a wide range of use. This research paper investigates these fascinating mathematical relationships, beginning with the connection between claw growth and logarithmic functions. Applying…

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Reaction Diffusion Patterns in Jaws of the Animal Kingdom

The endless number of patterns in nature is fascinating; they vary from spots on tigers, to lines on wood, to even teeth patterns in alligators. A mystery lies beneath all of this variety: how do these complex patterns arise and form such differing patterns? The origin of these patterns in…

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Mathematical Models of Molluscan Shell Patterns and Morphology

Mollusk shells’ mesmerizing diversity of forms stems from their variations in shape, features and patterns. While these forms are highly complex and diverse, research has aimed to establish an overarching model that explains the formation of these shell characteristics. This essay explores the mathematical models that capture these natural forms…

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