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The fundamental region is a shape such as a rectangle that is repeated to form the tessellation. [22] For example, a regular tessellation of the plane with squares has a meeting of four squares at every vertex. [18] The sides of the polygons are not necessarily identical to the edges of the tiles.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is 1/3; in apricot it is 2/5; in pear it is 3/8; in almond it is 5/13. [56] Animal behaviour can yield spirals; for example, acorn worms leave spiral fecal trails on the sea floor. [57]
Hyperbolic; Article Vertex configuration Schläfli symbol Image Snub tetrapentagonal tiling: 3 2.4.3.5 : sr{5,4} Snub tetrahexagonal tiling: 3 2.4.3.6 : sr{6,4} Snub tetraheptagonal tiling
Sunrise on the tessellated pavement at Eaglehawk Neck, Tasmania, illustrating the pan formation of tessellation. The most well known example of a tessellated pavement is the Tessellated Pavement that is found at Lufra, Eaglehawk Neck on the Tasman Peninsula of Tasmania. This tessellated pavement consists of a marine platform on the shore of ...
The state of a location is a finite number of real numbers. Time is also continuous, and the state evolves according to differential equations. One important example is reaction–diffusion textures, differential equations proposed by Alan Turing to explain how chemical reactions could create the stripes on zebras and spots on leopards. [55]
In pattern theory, devised by Ulf Grenander, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner. [27] In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of ...
Voronoi tessellations are interesting for spatial networks in the sense that they provide a natural representation model to which one can compare a real world network. Mixing space and topology; Examining the topology of the nodes and edges itself is another way to characterize networks.