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Beautiful Math, Part 5: Colorful Archimedean Tilings from Dynamical Systems.

Peichang Ouyang, Weiguo Zhao, Xuan Huang

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    |November 24, 2015
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    Summary
    This summary is machine-generated.

    This study introduces an invariant mapping method for creating colorful patterns on Archimedean tilings. These novel patterns exhibit both global crystallographic and local symmetries, inspired by early tiling art.

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    Area of Science:

    • Mathematics
    • Crystallography
    • Synthetic Organic Chemistry

    Background:

    • Tiling art, particularly with regular polygons, has a long history across civilizations.
    • Decorated regular tilings with symmetrical patterns are utilized in various decorative fields.
    • These geometric patterns serve as inspiration in scientific disciplines, including synthetic organic chemistry.

    Purpose of the Study:

    • To propose an invariant mapping method for generating colorful patterns on Archimedean tilings (1-uniform tilings).
    • To explore the creation of visually appealing and symmetrical patterns inspired by mathematical concepts.

    Main Methods:

    • Development of an invariant mapping technique.
    • Application of the method to Archimedean tilings.

    Main Results:

    • Successful creation of colorful patterns on Archimedean tilings.
    • The generated patterns possess both global crystallographic symmetry and local cyclic or dihedral symmetry.

    Conclusions:

    • The invariant mapping method offers a novel approach to designing symmetrical and visually rich patterns.
    • This work bridges the gap between decorative tiling art and scientific applications in pattern generation.