Plane Symmetry Group

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Plane Symmetry Group Examples

Tile 01 Plane Symmetry Group 01	Tile 02 Plane Symmetry Group 02	Tile 03 Plane Symmetry Group 03
Tile 04 Plane Symmetry Group 04	Tile 05 Plane Symmetry Group 05

The Plane Symmetry Group examples generate wallpaper patterns by passing the results of an attractor through a symmetry transformation that implements a plane symmetry group. A plane symmetry group is a mathematical classification of a pattern used to tile the plane. Each such pattern belongs to exactly one of the 17 plane symmetry groups. These are also referred to as wallpaper groups.

If we apply a symmetry transformation based on one of the plane symmetry groups to an attractor, we can tile the complex plane with the attractor. Depending on the size, position, and angle of the lattice associated with the symmetry group relative to the attractor, you can generate countless different patterns from a single attractor.

Plane symmetry groups are described in the book Symmetries of Culture - Theory and Practice of Plane Pattern Analysis by Dorothy K. Washburn and Donald W. Crowe.