There are only 17 ways to tile a flat surface perfectly
In short: While the world feels infinitely varied, the mathematics of repeating patterns is surprisingly finite. This video explores the Wallpaper Group, the set of rules governing every possible repeating pattern in a two-dimensional plane.
When we demand that a pattern must repeat infinitely in two directions—a property known as translational symmetry—we find that there are only 17 distinct ways to arrange rotations, mirror reflections, and glide reflections. These 17 possibilities form the 'Wallpaper Group.'
By understanding these underlying constraints, we can categorize every repeating design, from complex architectural motifs to the microscopic structures of crystals. It reveals a hidden mathematical order in the aesthetics of the physical world.
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Sources
- Summary by Intellect · source: The Beauty of Symmetry: An Introduction to the Wallpaper Group
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