Search results
Results From The WOW.Com Content Network
Many patterns in nature are formed by cracks in sheets of materials. These patterns can be described by Gilbert tessellations, [85] also known as random crack networks. [86] The Gilbert tessellation is a mathematical model for the formation of mudcracks, needle-like crystals, and similar structures.
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 ]
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 .
Reptiles depicts a desk upon which is a two dimensional drawing of a tessellated pattern of reptiles and hexagons, Escher's 1939 Regular Division of the Plane. [2] [3] [1] The reptiles at one edge of the drawing emerge into three dimensional reality, come to life and appear to crawl over a series of symbolic objects (a book on nature, a geometer's triangle, a three dimensional dodecahedron, a ...
The woodcut depicts a landscape mirrored horizontally with respect to the center of the image. It has two cities, each with an associated river and an interlocking pattern of birds gradually appearing towards the top of the image making a tessellation. These birds appear from the tiles of the landscape and become more detailed towards the ...
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals : implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its ...
The tessellations of zellij tilework in the Alhambra of Granada were also an important source of inspiration for the work of 20th-century Dutch artist M. C. Escher. [38] [39] [40] The tessellations in the mosaics are currently of interest in academic research in the mathematics of art. These studies require expertise not only in the fields of ...
A pattern is a regularity in the world, in human-made design, [1] or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.