The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy

@article{Smith2017TheTP,
  title={The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy},
  author={Cyril Stanley Smith and Paul Boucher},
  journal={Leonardo},
  year={2017},
  volume={20},
  pages={373 - 385}
}
A translation is given of Truchet’s 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half-colored tile in various orientations. It embodies an early representation of the principles of combinatorial theory and of crystallographic symmetry including color symmetry. Simple rules of the topology of separation and junction are used to extend Truchet’s concept of directional choice and, by relaxing symmetry rules, to generate diagrams illustrating field… 
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48 Citations
Highly Influential Citations
4
Background Citations
16
Methods Citations
5

48 Citations

Hyperbolic Truchet Tilings

About 300 years ago Sebastien Truchet systematically studied patterns that could be formed from square tiles that were divided by a diagonal into a white triangle and a black triangle. Other pattern…

Exploring symmetry in rosettes of Truchet tiles

ABSTRACT In 1704, the French priest Sébastien Truchet published a paper where he explored and counted patterns made up from a square divided by a diagonal line into two coloured parts, , now known as…

Enumerations of Hyperbolic Truchet Tiles

Sébastien Truchet was a pioneer in applying combinatorics to the study of regular patterns. He enumerated the patterns that could be formed from square tiles that were divided by a diagonal into a…

Truchet Tilings and Renormalization

The Truchet tiles are a pair of square tiles decorated by arcs. When the tiles are pieced together to form a Truchet tiling, these arcs join to form a family of simple curves in the plane. We…

Multi-Scale Truchet Patterns

This paper generalizes Smith’s tiles to infinite sets of tiles scaled by powers of 1/2, and uses the concept of a “winged” tile to show an easy way of producing multiscale patterns that show a large variety of emergent forms.

Truchet-tile structure of a topologically aperiodic metal–organic framework

When tiles decorated to lower their symmetry are joined together, they can form aperiodic and labyrinthine patterns. Such Truchet tilings offer an efficient mechanism of visual data storage related…

Infinitely Variable Tiling Patterns: From Truchet to Sol LeWitt Revisited

Patterns from Archimedean Tilings Using Generalized Truchet Tiles Decorated with Simple B´ ezier Curves

This paper explores a generalization of Truchet tiles by decorating tiles made from regular polygons with simple B´ ezier curves and considering more than one arc per side.

Chaos and Graphics Truchet curves and surfaces

Spanning tree contours, a special class of Truchet contour based upon a random spanning tree of a Truchet tiling’s underlying graph, are presented. This spanning tree method is extended to three…

Duotone Truchet-like tilings

This paper explores methods for colouring Truchet-like tiles, with an emphasis on the resulting visual patterns and designs. The methods are extended to non-square tilings that allow Truchet-like…

References

SHOWING 1-7 OF 7 REFERENCES

Structure in nature is a strategy for design

This book leads the designer in this "natural" direction, beyond the familiar limitations of the right angle and the cube and into a richer world of forms based on the triangle, the hexagon, and generalpolyhedra, as well as saddle polyhedra spanned by minimal continuous surfaces.

Celtic Art: The Methods of Construction

Celtic art has long been regarded as an enigma owing to its abstract, ikonographic and symbolic style. This offers a chronology of symbols and deals with zoomorphics (plant and human forms),…

Symmetry in Science and Art

A search for structure

Arabic Geometrical Pattern and Design

Color and symmetry

Islamic patterns : an analytical and cosmological approach

The point of departure the manifestation of shape magic squares pattern and cosmology the pentagon the tetractys the mathematics of two-dimensional space-filling the circle and cosmic rhythms…