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Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. [1] Early Greek philosophers studied pattern, with Plato ...
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). [1][2] More than a century later, the curve was discussed by Descartes (1638), and later extensively ...
Crisscrossing spirals of Aloe polyphylla. In botany, phyllotaxis (from Ancient Greek φύλλον (phúllon) 'leaf' and τάξις (táxis) 'arrangement') [ 1 ] or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature.
Approximations of this are found in nature. Spirals which do not fit into this scheme of the first 5 examples: A Cornu spiral has two asymptotic points. The spiral of Theodorus is a polygon. The Fibonacci Spiral consists of a sequence of circle arcs. The involute of a circle looks like an Archimedean, but is not: see Involute#Examples.
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by for plotting. [13] [predatory publisher]
Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern.
The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation. Some 20th-century artists and architects, including Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing it to be aesthetically pleasing. These uses often appear in ...
The honeycomb is a well-known example of tessellation in nature with its hexagonal cells. [82] In botany, the term "tessellate" describes a checkered pattern, for example on a flower petal, tree bark, or fruit. Flowers including the fritillary, [83] and some species of Colchicum, are characteristically tessellate. [84]