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Cells and cell complexes

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Many thing can be represented as cell complexes. Certainly, the number one is binary image, see Cell decomposition of images. There are however other important examples.

Cell Complexes Arising from Materials.

The paragraph below is taken from an abstract by Robert MacPherson.

The structure of two different sorts of materials leads to a cell decomposition of a region of 3-space:

  • Metals and ceramics are generally divided into individual crystals, typically of size ∼ 10^−5 meters, which are the cells of a cell complex.
  • Foams are a cell complex whose cells are the individual bubbles. Both of these situations have interesting two dimensional analogues, which give cell decompositions of a region of 2-space:
    • In very thin sheets of metals and ceramics, the grains are essentially two dimensional.
    • Bubbles trapped between two parallel sheets of glass are essentially two dimensional.

The structures of these cell complexes are key to understanding many of the properties of the material. The cell complexes are very large and complicated.

See also Tessellation.