Truchet Tile Art: Beauty and Math in Binary Choice
The Art of Truchet Tile Art
In the first of a series, we will look at the beauty of tiling and the mathematical underpinning of tile art. At first glance, it seems difficult to say that works of true beauty can be captured by squares set in patterns, but indeed they can. Truchet tiles are simply square tiles that can be solid, divided at an angle with a straight line, or divided at an angle with a curve. The straight lines give angularity, while the curved lines meander.
Truchet tilework dates to the 1700s. In 1704, French Dominican priest Sebastien Truchet, mathematician, engineer, and designer of the French canals, published “Mémoire sur les Combinaisons,” illustrating the many permutations that solid and dissected tiles could form. He was inspired by tilework in the canals.
Much later, Cyril Stanley Smith, a British metallurgist, added curved lines to Truchet-like tiles to explain the behavior of metal crystallization grain patterns at boundaries. Both men were working at the intersection of observation and art, finding that the rules governing physical structure and those governing beauty are often the same.
Due to the prohibition on human figure art in religious settings, Islamic artists turned to elaborate tilework to beautify mosques and other important civic and royal spaces. The complexity you see in the walls and ceilings emerges from repeated simple patterns, with each tile working with its neighbors to create an integrated whole.
This is the heart of what makes Truchet tile art mathematically interesting: the pattern has no memory of the whole, only the logic of its behavior, yet something with structure and often beauty emerges anyway.
The Art of Tile
Explore the mathematics behind Truchet tiles, from a French Dominican priest in 1704 to Islamic tilework. Discover how a single choice creates patterns of pure beauty.
Order Set by Single Choice
That relationship between local randomness and global order has a measure. The Hurst exponent describes the degree of persistence in a pattern, the degree to which neighboring elements tend to resemble or continue each other.
A purely random Truchet grid, where each tile is placed without regard to its neighbors, sits near H = 0.5. When order is imposed, diagonals assemble in directions, and the Hurst value rises. The pattern has a memory. We have written about the Hurst exponent in the context of language and literary style, but it also applies to art.
M.C. Escher, another artist who worked with tilework, was inspired by Islamic tilework at the Alhambra Palace in Granada, Spain, during his visits there in 1922 and 1936. He kept careful notebooks of what he observed and considered them one of his biggest sources of inspiration. He returned to those notebooks throughout his career, using the logic of repeating geometry to develop animal and figure transformations and tessellations.
The leap from Truchet to Escher is shorter than it looks: both begin with a square, a rule, and a rotation.
If you would like to try your hand at tessellations, our tool lets you build patterns of your own tessellation. The Truchet Studio lets you explore Truchet tile art in arc tiles, diagonal tiles, solid tiles, symmetry, and path topology through a single choice.