Definitions A tessellation is formed when a shape is repeated indefinitely, covering a plane with no gaps or overlaps. "To create a mosaic design with little pieces of stone or glass." "The pattern created by gluing together pieces of paper with rubber cement." "A picture made by tiling images downloaded from the Internet."

Tessellations are common in nature and can be seen for example in the patterns on seeds or shells. They are also used in architecture to decorate walls and ceilings. Modern artists use tessellations as a basis for **their work**. In mathematics, a tessellation is an infinite repetition of **a simple form** which covers all of space without **any overlapping** or gap.

In photography, a tessellation is a pictorial composition in which adjacent parts of the image are separated by clear boundaries. The picture is made up of small elements that are similar in size and shape. These elements are called tiles. The photographer then arranges these tiles in a regular pattern to create the effect of a larger piece of artwork.

Some examples of photographs that are considered tessellations include Edward Weston's Flatbed Truck (1932) and Lee Friedlander's Hudson River Series (1977-1983). Both photographers used vehicles as inspiration for **their works**.

A pattern of shapes that fit together wonderfully! Tessellation (or tiling) is the process of covering a surface with a pattern of flat objects with no overlaps or gaps. The term comes from the Latin word for "tessera", which is a piece used in mosaic work.

Tessellations can be divided up into five general categories: repetitive, non-repetitive geometric, fractal, cellular.

Repetitive tessellations use the same unit shape over and over again to create a pattern. These include triangular pyramids, hexagons, and circles. Non-repetitive tessellations use **different shapes** at **each location**. Examples include squares and lines. Geometric fractals are repetitive patterns that look like they have self-similarity properties, such as snowflakes and coastlines. Cellular tessellations consist of a mesh of cells where each cell is filled with the appropriate shape. For example, a honeycomb sheet is made up of hexagonal cells.

People have been tessellating shapes since **at least 300 B.C.**, when Greek mathematician Euclid described a method for constructing regular polygons. In the 17th century, Swiss mathematician Jacob Bernoulli invented a device called the binaire, which could generate **two simultaneous random numbers**.

A tessellation pattern is one that is made up of forms that do not have any gaps or overlaps. Tessellations can be created using simple geometric forms (such as squares and triangles) or with much more complicated or irregular shapes (such as stylized birds or fish) that have been engineered to fit together neatly in a repeating pattern. The most common example of a tessellation pattern is the checkerboard.

Simple tessellations are easy to create with **just a few basic figures** such as squares and triangles. They often use symmetry to reduce the number of required pieces. For example, if you divide the square into four identical pieces, then when put back together they will form **another square**. There are many simple ways to divide a square or other shape into equal parts; for example, cutting it into nine similar pieces or placing it inside another smaller square. You can also use this method to divide **other polygons**, such as triangles.

In mathematics, physics, and engineering, a tessellation is the division of a plane into regular polygonal cells. The simplest case is where each cell is divided into two congruent and adjacent sides. A tessellation implies repetition of an original pattern, which leads to the name "tesselation." In geometry and topology, tessellations consist of faces (two-dimensional surfaces), edges (one-dimensional lines), vertices (three-dimensional points), and cells (three-dimensional regions).

Tessellations are continuous patterns composed of repeated forms that completely cover a surface without overlapping or leaving any gaps. They can be geometric or abstract, but they all have one thing in common: each part of the pattern is identical to every other part.

MC Escher was a Dutch artist who created visual illusions that play with our perception of reality and gravity. He was famous for his drawings and prints that use this kind of art to demonstrate the similarities we see between different objects. One of these demonstrations is tessellations; patterns formed by interlocking triangles that show how complex you can make something really simple if you look at it from a different angle.

In mathematics, physics, and engineering, tessellations are geometrical patterns formed by the repetition of **simpler shapes** (cells), without overlap. The term comes from the Greek word τέσσελος (tesselos), meaning "something twisted," referring to the shape of some Roman coins. Mathematics provides many methods for **generating tessellations**; see List of regular polytopes for examples. Physical applications include **the periodic structure** of crystals and glass, the skin of animals, and the shells of mollusks.

Tessellation A pattern created by transforming geometric shapes in various ways. If a form is a regular geometric figure and the sides all fit together exactly with no gaps, it will tessellate. For example, the square and the pentagon are examples of two-dimensional tessellating shapes.

There are also three-dimensional tessellating shapes such as cubes and pyramids. A cube can be split into eight squares and a pyramid into six triangles. These ten shapes can be joined together to make a tiling of the space around them.

The word "tessel" comes from Latin meaning "to cut in slices." Thus, a tessellation is a pattern made up of **flat or curved polygons** that are sliced across like **a pie crust** or cake.

In mathematics, a tessellation is any covering of a plane or other surface by **identical copies** of **a simple shape**, without gaps or overlaps. The term is applied specifically to coverings where these copies are congruent and have nonempty intersections. That is, no point of the original shape is left uncovered.

A well-known example is the tetris game. Here, rows of blocks fall from the top of the screen and must be arranged so as to fill the space below.

Robert Fathauer's Tessellation Art A tessellation is a collection of forms called tiles that fit together to cover the mathematical plane without gaps or overlaps. M.C. Escher, a Dutch graphic designer, gained famous for **his tessellations**, in which the individual tiles represent **recognized patterns** such as birds and fish. He used this technique extensively in his prints.

Tessellations have been made by many artists throughout history. Some modern examples can be seen in public spaces around cities worldwide. None of these tessellations are by Robert Fathauer but they are inspired by his work.

Robert Fathauer was a German artist who created some of the first known abstract paintings. In 2001, he received international attention when it was discovered that several of his works were sold at auction houses with fake prices. The fakes were determined by laboratory analysis to be worth only $1 per square foot! The real price of the paintings has never been disclosed.

Fathauer died in 2004 at the age of 94.

Some people may not know that the man who designed **the Mercedes-Benz logo** also did some amazing artwork. William Morris was a British artist who founded **the design movement** known as "Japonism". He traveled to Japan several times and painted what he saw there, bringing back photos and drawings that show how Japanese culture influenced his designs. One of his paintings is even on display in **the London Museum**.