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Beautiful Math, Part 5: Colorful Archimedean Tilings from Dynamical Systems
IEEE Computer Graphics and Applications
|November 24, 2015
Summary
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.
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.
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