Aperiodic tilings

Aperiodic tiling

An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings. The Penrose tilings are the best-known examples of aperiodic tilings. Aperiodic tilings serve as mathematical models forquasicrystals, physical solids that were discovered in 1982 by Dan Shechtman who subsequently won the Nobel prize in 2011. However, the specific local structure of these materials is still poorly understood. Several methods for constructing aperiodic tilings are known. (Wikipedia).

Aperiodic tiling
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Lots of Aperiodic Sets of Tiles! – Chaim Goodman-Strauss

Inspired by Martin Gardner's writings on aperiodic tiling, we present thousands of new examples, organized into lots.

From playlist G4G12 Videos

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Triangle tilings

(5,3,2) triangle tiling: http://shpws.me/NW2E (7,3,2) triangle tiling (small): http://shpws.me/NW3A (6,3,2) triangle tiling: http://shpws.me/NW3H (4,3,2) triangle tiling: http://shpws.me/NW3K (3,3,2) triangle tiling: http://shpws.me/NW3J (4,4,2) triangle tiling: http://shpws.me/NW3M

From playlist 3D printing

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Introduction to Tiling Theory

In this mini-lecture, we explore tilings found in everyday life and give the mathematical definition of a tiling. In particular, we think about: (i) traditional Islamic tilings; (ii) floor, wallpaper, pavement, and architectural tilings; (iii) the three regular tilings using either equilat

From playlist Maths

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Regular polyhedra

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.

From playlist 3D printing

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Using a set of points determine if the figure is a parallelogram using the midpoint formula

πŸ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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What is an isosceles triangle

πŸ‘‰ Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

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What is an equilateral triangle

πŸ‘‰ Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

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What is an obtuse triangle

πŸ‘‰ Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

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Cookie Shapes!

Avoiding math to have a relaxing Saturday with friends. Links to everyone's cool stuff below: Gwen Fisher: http://www.beadinfinitum.com/ She also has a blog: http://gwenbeads.blogspot.com/ Also buy everything from her etsy shop before someone else does: https://www.etsy.com/shop/gwenbead

From playlist Thanksgiving: Edible Math

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6D minecraft? - Aperiodic Voxel Game devlog#1

The intro music is aperiodic too, played by me on a broken cello. The rest of the background music was a public domain recording of Beethoven Sonata no. 1, played by Daniel Veesey. Development for this game started in Processing, but I felt I was writing many lines of Java code for things

From playlist Summer of Math Exposition Youtube Videos

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The Beauty of Symmetry: An Introduction to the Wallpaper Group

Keep exploring at β–Ί https://brilliant.org/TreforBazett. Get started for free for 30 days β€” and the first 200 people get 20% off an annual premium subscription! Resources used in the video: Web app to generate all 17 wallpapers: https://math.hws.edu/eck/js/symmetry/wallpaper.html Lots of i

From playlist Cool Math Series

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Determine if a set of points is a trapezoid or not

πŸ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Ayliean MacDonald - The Pentagon: A User’s Guide - CoM Oct 2021

Regular pentagons throw a spanner in the works when it comes to tessellation but don’t let that one case tarnish the good name of the pentagon! Come along as we explore the 15 irregular pentagons which do tile the plane, journey through five fold symmetry, make a quick pit stop to look at

From playlist Celebration of Mind 2021

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Footloose on a tiled trail - Exploring repeating patterns by C S Aravinda

When: 4pm to 6pm Sunday, 19 February 2017 WHERE: Jawaharlal Nehru Planetarium, Bengaluru Regularly repeating patterns are commonplace around us, on tile-laid pavements, on tapestry designs, on window grills, on rangolis and so on. Exploring newer and newer basic patterns to create novel

From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)

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How to Use the Mathigon Aperiodic Monotile Creator

Link to @Mathigon #Polypad: https://mathigon.org/polypad/8kVqVH2Mor6JTQ Construction created by Dan Anderson: https://twitter.com/dandersod

From playlist Mathigon Demos and Ideas

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How to Use This GeoGebra Aperiodic Monotile Creator

Link: https://www.geogebra.org/m/gq5mtkfa

From playlist Geometry: Dynamic Interactives!

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Determine if a set of points is a parallelogram by using the slope formula

πŸ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

Related pages

Lie group | Penrose tiling | Undecidable problem | Meyer set | Aperiodic tiling | Prototile | Robert Ammann | Nicolaas Govert de Bruijn | Tessellation | Quasicrystal | Substitution tiling | List of aperiodic sets of tiles | Pinwheel tiling | Graph paper | Beatty sequence | Amenable group | Hao Wang (academic) | Sturmian word | Aperiodic set of prototiles | Girih tiles