Sebastien Truchet
Encyclopedia
Sébastien Truchet was an eclectic Dominican
Father born in Lyon
and lived in Louis XIV
times. He is known for being active in areas such as mathematics
, hydraulics
, graphics
, typography
, and for many inventions.
As typographer he studied for the Description des Métiers the proportions of typefaces of "Roman Du Roi" character (also known as Grandjean character), from which descends directly the "Times New Roman" and which inspired Pierre Simon Fournier
, the Didot
and Giovanni Battista Bodoni. It was the first scientific work on typefaces, and on this work is based the concept of typographic point
(whose first definition is due to French typographer Pierre Simon Fournier
in year 1737).
As hydraulics
expert he designed most of French channels.
As inventor he is known for sundial
s, weapon
s and tools for transplanting
large trees within the Versailles
gardens.
As mathematician
and designer
he worked on plane coverage using tile
able elements.
Some examples of surface filling made tiling such a pattern
.
With a scheme:
With random placement:
From a mathematical point of view this is the central theme. From an artistic point of view if we change the basic shape to a more complex one, we can get very nice combinations. For example, using the following pattern or its inverse:
We have such a tiling:
The lines in this pattern are used in the proof that certain types of Langton's ant
will always walk on symmetrical paths.
Fournier
resumed Truchet work and proposed alternative patterns:
With Fournier pattern we obtain:
As a curiosity we remember that a simple maze could be generated tiling a white square with a black diagonal:
Truchet tilings are used for walls
, floors
, marquetry
, rear of Tarot
ées, wallpapers and other contexts.
Many software programs generate random plane coverage with such a tiling, and some board games are based on this fascinating part of Truchet work.
Dominican Order
The Order of Preachers , after the 15th century more commonly known as the Dominican Order or Dominicans, is a Catholic religious order founded by Saint Dominic and approved by Pope Honorius III on 22 December 1216 in France...
Father born in Lyon
Lyon
Lyon , is a city in east-central France in the Rhône-Alpes region, situated between Paris and Marseille. Lyon is located at from Paris, from Marseille, from Geneva, from Turin, and from Barcelona. The residents of the city are called Lyonnais....
and lived in Louis XIV
Louis XIV of France
Louis XIV , known as Louis the Great or the Sun King , was a Bourbon monarch who ruled as King of France and Navarre. His reign, from 1643 to his death in 1715, began at the age of four and lasted seventy-two years, three months, and eighteen days...
times. He is known for being active in areas such as mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, hydraulics
Hydraulics
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...
, graphics
Graphics
Graphics are visual presentations on some surface, such as a wall, canvas, computer screen, paper, or stone to brand, inform, illustrate, or entertain. Examples are photographs, drawings, Line Art, graphs, diagrams, typography, numbers, symbols, geometric designs, maps, engineering drawings,or...
, typography
Typography
Typography is the art and technique of arranging type in order to make language visible. The arrangement of type involves the selection of typefaces, point size, line length, leading , adjusting the spaces between groups of letters and adjusting the space between pairs of letters...
, and for many inventions.
As typographer he studied for the Description des Métiers the proportions of typefaces of "Roman Du Roi" character (also known as Grandjean character), from which descends directly the "Times New Roman" and which inspired Pierre Simon Fournier
Pierre Simon Fournier
Pierre Simon Fournier was a French mid-18th century punch-cutter, typefounder and typographic theoretician. He was both a collector and originator of types”. Fournier's contributions to printing were his creation of initials and ornaments, his design of letters, and his standardization of type...
, the Didot
Didot
Didot is the name of a family of French printers, punch-cutters and publishers. Through its achievements and advancements in printing, publishing and typography, the family has lent its name to typographic measurements developed by François-Ambroise Didot and the Didot typeface developed by Firmin...
and Giovanni Battista Bodoni. It was the first scientific work on typefaces, and on this work is based the concept of typographic point
Point (typography)
In typography, a point is the smallest unit of measure, being a subdivision of the larger pica. It is commonly abbreviated as pt. The point has long been the usual unit for measuring font size and leading and other minute items on a printed page....
(whose first definition is due to French typographer Pierre Simon Fournier
Pierre Simon Fournier
Pierre Simon Fournier was a French mid-18th century punch-cutter, typefounder and typographic theoretician. He was both a collector and originator of types”. Fournier's contributions to printing were his creation of initials and ornaments, his design of letters, and his standardization of type...
in year 1737).
As hydraulics
Hydraulics
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...
expert he designed most of French channels.
As inventor he is known for sundial
Sundial
A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a...
s, weapon
Weapon
A weapon, arm, or armament is a tool or instrument used with the aim of causing damage or harm to living beings or artificial structures or systems...
s and tools for transplanting
Transplanting
For botanical organ transplant, see GraftingIn agriculture and gardening, transplanting or replanting is the technique of moving a plant from one location to another. Most often this takes the form of starting a plant from seed in optimal conditions, such as in a greenhouse or protected nursery...
large trees within the Versailles
Versailles
Versailles , a city renowned for its château, the Palace of Versailles, was the de facto capital of the kingdom of France for over a century, from 1682 to 1789. It is now a wealthy suburb of Paris and remains an important administrative and judicial centre...
gardens.
As mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and designer
Designer
A designer is a person who designs. More formally, a designer is an agent that "specifies the structural properties of a design object". In practice, anyone who creates tangible or intangible objects, such as consumer products, processes, laws, games and graphics, is referred to as a...
he worked on plane coverage using tile
Tile
A tile is a manufactured piece of hard-wearing material such as ceramic, stone, metal, or even glass. Tiles are generally used for covering roofs, floors, walls, showers, or other objects such as tabletops...
able elements.
Truchet tiles
His work on plane coverage used a single tile that could be rotated in the four main directions. An example of Truchet tiles:Some examples of surface filling made tiling such a pattern
Pattern
A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects.These elements repeat in a predictable manner...
.
With a scheme:
With random placement:
From a mathematical point of view this is the central theme. From an artistic point of view if we change the basic shape to a more complex one, we can get very nice combinations. For example, using the following pattern or its inverse:
We have such a tiling:
The lines in this pattern are used in the proof that certain types of Langton's ant
Langton's ant
Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complicated emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The universality of Langton's ant was proven in 2000...
will always walk on symmetrical paths.
Fournier
Pierre Simon Fournier
Pierre Simon Fournier was a French mid-18th century punch-cutter, typefounder and typographic theoretician. He was both a collector and originator of types”. Fournier's contributions to printing were his creation of initials and ornaments, his design of letters, and his standardization of type...
resumed Truchet work and proposed alternative patterns:
With Fournier pattern we obtain:
As a curiosity we remember that a simple maze could be generated tiling a white square with a black diagonal:
Walls
- Other uses :*Wall's , a company that makes ice cream*Wall's sausages, a British sausage brand*Walls, an episode of Power Rangers S.P.D.- Music :*Walls EP, a 2005 album by The Red Paintings*Walls , 2007...
, floors
Flooring
Flooring is the general term for a permanent covering of a floor, or for the work of installing such a floor covering. Floor covering is a term to generically describe any finish material applied over a floor structure to provide a walking surface...
, marquetry
Marquetry
Marquetry is the art and craft of applying pieces of veneer to a structure to form decorative patterns, designs or pictures. The technique may be applied to case furniture or even seat furniture, to decorative small objects with smooth, veneerable surfaces or to freestanding pictorial panels...
, rear of Tarot
Tarot
The tarot |trionfi]] and later as tarocchi, tarock, and others) is a pack of cards , used from the mid-15th century in various parts of Europe to play a group of card games such as Italian tarocchini and French tarot...
ées, wallpapers and other contexts.
Many software programs generate random plane coverage with such a tiling, and some board games are based on this fascinating part of Truchet work.
See also
- Girih tilesGirih tilesGirih tiles are a set of five tiles that were used in the creation of tiling patterns for decoration of buildings in Islamic architecture...
- TessellationTessellationA tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...
- Tilings of regular polygons
- Wallpaper groupWallpaper groupA wallpaper group is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art...
- Wang tiles
External links
- Sébastien Truchet biography: http://jacques-andre.fr/faqtypo/truchet/index.html
- Mathworld reference: http://mathworld.wolfram.com/TruchetTiling.html
- Truchet in 2D and 3D: http://local.wasp.uwa.edu.au/~pbourke/texture_colour/periodic/
- More informations on Sébastien Truchet: http://www.tug.org/TUGboat/Articles/tb20-1/tb62andr.pdf
- Deepening on "Roman Du Roi" font: http://ilovetypography.com/2008/01/17/type-terms-transitional-type/
- Javascript animation: http://perso.orange.fr/jean-paul.davalan/divers/truchet/truc.html