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Self-similarity can be found in nature, as well. To the right is a mathematically generated, perfectly self-similar image of a fern, which bears a marked resemblance to natural ferns. Other plants, such as Romanesco broccoli, exhibit strong self-similarity.
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 ]
In these cases, the reason may be construction from expanding similar shapes, as is the case for polygonal figures. Logarithmic spiral beaches can form as the result of wave refraction and diffraction by the coast. Half Moon Bay (California) is an example of such a type of beach. [15]
The recursive nature of some patterns is obvious in certain examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. Similarly, random fractals have been used to describe/create many highly irregular real-world objects, such as coastlines and mountains.
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Convergent evolution—the repeated evolution of similar traits in multiple lineages which all ancestrally lack the trait—is rife in nature, as illustrated by the examples below. The ultimate cause of convergence is usually a similar evolutionary biome , as similar environments will select for similar traits in any species occupying the same ...
The pattern of similarity was interpreted as part of the static great chain of being through the mediaeval and early modern periods: it was not then seen as implying evolutionary change. In the German Naturphilosophie tradition, homology was of special interest as demonstrating unity in nature.
Weeders do not want to select weeds and their seeds that look increasingly like cultivated plants, yet there is no other option. For example, early barnyard grass, Echinochloa oryzoides, is a weed in rice fields and looks similar to rice; its seeds are often mixed in rice and have become difficult to separate through Vavilovian mimicry. [96]