Tessellation is a technique used in mathematics, art, and architecture where a two-dimensional plane is covered with repeating shapes without any gaps or overlaps.
The repeating shapes are called tessellation patterns or tessellations, and they are typically made up of regular polyggonal shapes such as squares, triangles, or hexagons.
Tessellation has been used for centuries to create illusions, decorative designs, to build tiled floors and walls, and more recently in computer graphics and video games. In mathematics, tessellations are studied as a part of geometry, where they are used to explore concepts such as symmetry and repeat patterns.
Table of Contents for Tessellation Illusions
- How do Tessellation Illusions work?
- Versions of Tessellation Illusions
- Illusions like the Tessellation Illusions
- Discovery of Tessellation Illusions
- References and Resources
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How do Tessellation Illusions work?
Tessellation works by repeating a single shape, or a set of shapes, in a regular pattern to cover a two-dimensional plane without any gaps or overlaps. The key to creating a tessellation is to find a shape, or set of shapes, that can be repeated in such a way that the edges of each shape meet and fit together seamlessly. The most common shapes used in tessellation are regular polyggonal shapes such as squares, triangles, and hexagons.
In order to create a tessellation, the shape or shapes must be transformed in some way so that they fit together perfectly. For example, the shapes can be rotated, reflected, or scaled to create the tessellation pattern. This transformation is what allows the shapes to repeat seamlessly and form a tessellation.
There are several types of tessellations, including periodic tessellations, which repeat in a regular pattern, and non-periodic tessellations, which do not repeat in a regular pattern. Each type of tessellation has its own unique properties and can be used to create different effects. Whether used for practical purposes such as floor or wall tiles, or for artistic expression, tessellation is a powerful technique for creating repeating patterns in two-dimensional space.
Versions of Tessellation Illusions
The following are some alternate versions of Tessellation Illusions:
Illusions like Tessellation Illusions
Tessellation is not an illusion by itself/ It is a real physical phenomenon that occurs when a two-dimensional plane is covered with repeating shapes without any gaps or overlaps. However, tessellations can be used to create optical illusions, such as when an artist creates a tessellation pattern that gives the impression of three-dimensional shapes or motions. In this sense, tessellation can be used as a tool to create illusions, but the tessellation itself is not an illusion.
There are several illusions that are similar to tessellation or use tessellation as a technique. Here are some examples:
- Escher-style tessellations: M.C. Escher was a Dutch artist who was famous for creating tessellation patterns that appeared to form impossible constructions or scenes. These tessellations often use repetition and symmetry to create optical illusions.
- Tessellated moire patterns: A moire pattern is created when two repeating patterns overlap and interact with each other. When tessellation patterns are used to create moire patterns, the result is a mesmerizing optical illusion.
- Tiling illusions: Tiling illusions are similar to tessellations, but they use different shapes and patterns to create the illusion of depth, movement, or three-dimensionality. For example, a tiling illusion may use squares of different sizes or colors to create the illusion of a curved surface.
- Kaleidoscopic patterns: Kaleidoscopic patterns are created by repeating a set of shapes in a symmetrical pattern, often with reflections. Kaleidoscopic patterns can be created using tessellation shapes, and they are often used to create mesmerizing optical illusions.
The following are some illusions that are similar:.
The Rotating Snakes is a peripheral drift illusion that consists of a grid of shapes, with some of them appearing to be rotating or undulating. The illusion is created by the interaction of the shapes with the neural processing of the visual system.
The Moiré pattern illusion: This illusion is created by superimposing two similar patterns on top of each other, such as a grid of lines or circles. The resulting pattern appears to be moving or changing.
The Scintillating Grid Illusion, in which a grid of black and white squares appears to pulsate or “breathe” when viewed from the periphery of the image.
The Zöllner illusion is a visual illusion in which parallel lines appear to be angled due to the presence of intersecting lines.
The illusion is often used to study the brain’s perception of shape and spatial relationships. It is considered one of the most powerful and striking examples of a geometrical-optical illusion. The perception of the illusion can be explained by the brain’s tendency to group lines together based on their similarity in direction and spacing, which can lead to an overestimation of the angle between the parallel lines.
The Cafe Wall Illusion is a geometric optical illusion that is created by the alignment of parallel lines in a checkerboard pattern. The parallel lines appear to be tilted or slanted, even though they are actually straight.
This illusion is caused by the interaction of the lines with the edges of the squares in the checkerboard pattern, which creates the illusion of depth and perspective.
The Wundt illusion is an optical illusion produces an inversed effect compared to the Hering Illusion. The vertical lines are both straight, but they may look as if they are curved inwards.
The following MC Escher creations employ tessellation:
“Relativity” – A lithograph that depicts a world where gravity and direction are relative and interchangeable.
“Waterfall” – A woodcut print that features a seemingly impossible flow of water that cascades upward and through a gear system before falling back down into a pool.
“Sky and Water I” – A woodcut print that features an intricate pattern of birds and fish that seem to transform into each other.
“Day and Night” – A woodcut print that features a world where the boundary between day and night is fluid and interchangeable.
“Metamorphosis III” – A lithograph that features a series of interlocking shapes that seem to change and transform into one another.
“Hands Drawing Hands” – A lithograph that features a series of hands drawing hands, creating a never-ending cycle of creation.
Discovery of Tessellation
Tessellation has been used by many cultures throughout history, so it’s difficult to attribute its discovery to a single person. Some of the earliest known examples of tessellation can be found in ancient Egyptian and Greek art, where tessellated patterns were used to decorate floors and walls.
However, the artist who is perhaps most closely associated with tessellation is M.C. Escher, a Dutch artist who lived from 1898 to 1972. Escher was famous for his mathematically inspired art, which often featured tessellation patterns that appeared to form impossible constructions or scenes. He popularized tessellation as an art form and inspired a generation of artists and mathematicians to explore the possibilities of this technique.
Through his work, Escher helped to bring tessellation to the attention of a wider audience and demonstrated its potential as a tool for artistic expression and visual storytelling. Today, tessellation is widely recognized as an important element of mathematical and artistic heritage, and it continues to inspire new generations of artists and mathematicians alike.
References and Resources
Check out our complete list of illusions.
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