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  2. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    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]

  3. Patterns in nature - Wikipedia

    en.wikipedia.org/wiki/Patterns_in_nature

    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 ]

  4. Voronoi diagram - Wikipedia

    en.wikipedia.org/wiki/Voronoi_diagram

    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 .

  5. Cellular automaton - Wikipedia

    en.wikipedia.org/wiki/Cellular_automaton

    In 1969, German computer pioneer Konrad Zuse published his book Calculating Space, proposing that the physical laws of the universe are discrete by nature, and that the entire universe is the output of a deterministic computation on a single cellular automaton; "Zuse's Theory" became the foundation of the field of study called digital physics. [21]

  6. Penrose tiling - Wikipedia

    en.wikipedia.org/wiki/Penrose_tiling

    Concretely, if A S has side lengths (1, 1, φ), then A L has side lengths (φ, φ, 1). B-tiles can be related to such A-tiles in two ways: If B S has the same size as A L then B L is an enlarged version φ A S of A S, with side lengths (φ, φ, φ 2 = 1 + φ) – this decomposes into an A L tile and A S tile joined along a common side of length 1.

  7. List of tessellations - Wikipedia

    en.wikipedia.org/wiki/List_of_tessellations

    This is a list of tessellations. This list is incomplete; you can help by ... Regular Spherical (n=1, 2, 3, ...) Article Vertex configuration Schläfli symbol Image ...

  8. Architectonic and catoptric tessellation - Wikipedia

    en.wikipedia.org/wiki/Architectonic_and...

    Ref. [1] indices Symmetry Architectonic tessellation Catoptric tessellation Name Coxeter diagram Image Vertex figure Image Cells Name Cell Vertex figures; J 11,15 A 1 W 1 G 22 δ 4 nc [4,3,4] Cubille (Cubic honeycomb) Octahedron, Cubille: Cube, J 12,32 A 15 W 14 G 7 t 1 δ 4 nc [4,3,4] Cuboctahedrille (Rectified cubic honeycomb) Cuboid, Oblate ...

  9. Bitruncated cubic honeycomb - Wikipedia

    en.wikipedia.org/wiki/Bitruncated_cubic_honeycomb

    The honeycomb represents the permutohedron tessellation for 3-space. The coordinates of the vertices for one octahedron represent a hyperplane of integers in 4-space, specifically permutations of (1,2,3,4). The tessellation is formed by translated copies within the hyperplane. The tessellation is the highest tessellation of parallelohedrons in ...