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Tessellations
Websites
Adobe Illustrator plug-in that automates creation of surface designs and ornaments based on seventeen wallpaper groups. On-line purchase.
http://www.artlandia.com/SymmetryWorks
A collection of links.
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The Geometry Junkyard: Tilings One way to define a tiling is a partition of an infinite space (usually Euclidean) into pieces having a finite number of distinct shapes. Tilings can be divided into two types, periodic and aperiodic, depending on whether they have any...Compiled by Suzanne Alejandre for the Math Forum.
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Math Forum: Tessellation Links Suzanne Alejandre Tessellations are fun for elementary, middle school and high school students, and they also have practical applications. The sites listed on this page provide more insight into the topic for the following levels: E [Elementary] MS [Middle School] HS [High...An introduction to tessellations explaining the basic underlying mathematics, and with many examples from real life.
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Totally Tessellated ...A summary of the history behind the Penrose tiling in the math department at Miami university.
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The Penrose Tiling at Miami University Mathematics and among the featured speakers were John Conway, Elwyn Berlekamp, David Klarner, Doris Schattschneider, L eon Bankoff, and Wolfgang Haken. Conway had just published his book, On Numbers and Games, and Haken had announced a computer-assisted proof of the...Graphics and references.
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tilepent Grunbaum for assistance with this page. An article by Doris Schattschneider about pentagons is available here. Her interactive tiling page is here. John Savard has put together a beautiful page about a pentagonal tiling system originally discovered by Kepler here....Andrew Crompton's tiling and tessellation images.
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crompton tessellations Viewing this page requires a browser capable of displaying frames....Escher-like tessellations.
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Hop's Escher Tessellation Tiles Too many thumbnails take a long time to download. If you'd still like to use the thumbnail links they're at Tile Thumbnail Gallery 1 and Tile Thumbnail Gallery 2 Or you can use the text links below. Dog and Bug...Explanations and graphics.
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Hyperbolic Tessellations You can now create your own hyperbolic tessellations. See the Java applet page A regular tessellation, or tiling, is a covering of the plane by regular polygons so that the same number of polygons meet at each vertex. No doubt,...Examples and source code.
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Understanding symmetry is essential to the understanding of Escher art and understanding symmetry involves a familiarity with the movements that mathematicians call transformations Jill and Walter Britton) Click to view the Step by Step Tessellations for a detailed explanation on...Examples and Java applets.
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Tessellations and Periodic Drawings, Tiling, Wallpaper, JAVA Graphics, Patchwork, Quilt, textile design, katagami, stencils, Lattice Windows, Wood Lattice, multicultural math, puzzle quilts, Islamic pattern, connections, Infinity, fretwork pattern, symmetry, concrete paving, Color Tiles, Regular Division, Arts and Crafts, Celtic design and pattern, Regular Patterns, Two Dimensional Symmetry, Geometry Challenges, Motif, Mathematical Mosaics, Latticework, etched glass, Japanese quilt, Japanese textile design, Pattern design, sashiko, chiyogami, temari, Design is part of the human consciousness. Culture is how people see and do things from a historical prospective. The images shown here with the Java graphics are rooted in thousands of years of use and living. Escher began his...Examples in traditional Japanese patterns.
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Seventeen Kinds of Wallpaper Patterns We find such repeated patterns on wallpaper everywhere in our daily life. Have you considered how many kinds of repetitions there are for patterns on a plane? Do you think there are five or six kinds? No, there are seventeen!...Links to activities and other resources.
http://www.camosun.bc.ca/~jbritton/jbsymteslk.htm
Original tessellating desktop wallpaper tiles.
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Tessellating Wallpaper Patterns Please feel free to use any of the graphics on this site. To set an image as your desktop wallpaper, right click on it and choose Set as Wallpaper from the menu. Home Page 2 Non-Tessellating Patterns Wallpaper Symmetry Groups...By Marjorie Rice. Pentagons that tile the plane: details and links.
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Listing of directory tessellations/ Listing of directory tessellations/ Listing of directory tessellations/ FileName Last Modified Size...Tiling from the mathematical and historical viewpoint by Steve Edwards. Provides a number of examples of various types of tiles that tile the plane and includes periodic tiling plus Penrose's aperiodic tiles.
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Tiling Plane and Fancy Tiling from the mathematical and historical viewpoint Site maintained and 2000-2004 Steve Edwards. All otherwise unattributed images© Steve Edwards email: sedwards@spsu.edu home page Southern Polytechnic State University, Marietta GA 30060...A company selling foam puzzles, many based on planar tessellations (tilings) and fractals.
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tessellations.com front door page If this message does not disappear in a few seconds, click here to enter...This chaotic tiling consists of two equilateral pentagons, with angles (80, 160, 60, 140, 100) and (40, 200, 60, 100, 140). Sets are for sale.
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chaotile This header plots the critical line of the Riemann Zeta Function. A complete understanding wins a $1,000,000 prize Main Links Orders Post Next Page Next 10 CHAOS TILES ARE NOW ON SALE! You can see the rules for the game...Description of a class project.
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SketchPad Unit Index Standards geometry provides an opportunity for students to experience the creative interplay between mathematics and art. This project is specifically designed to allow students to demonstrate their ability to create art using transformational geometry. Many high school students are familiar...Web text by Ana Kozomara.
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Index DISCRETE PLANE SYMMETRY GROUPS Ana Kozomara...Tessellation images and software.
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Alex Bateman's Origami Page. Welcome to my humble corner of the web. I tend to fold and design my own models, but my favourite creators are Robert Lang and Nick Robinson. During recent years I have moved from designing origami animals to geometric designs....Compiled by Yoshiaki Araki.
http://www.sfc.keio.ac.jp/~aly/escher/
Includes: Symmetric icons and fractals; Quilts and planar repeating patterns; Colored wallpaper patterns.
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Gallery of Symmetric Chaos page This collection of images is divided into the following groups: Some recent work Symmetric Icons. Symmetric Fractals. Repeating patterns (or Quilts Logos (old) One and two color repeating patterns (old) The repeating patterns directory contains the directories Hexagonal Quilts and...University of Houston. Graphics and resources in symmetry and tiling.
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Symmetry, Chaos and Field Homepage Primary research interests: ergodic theory, coupled cell systems, the geometric theory of dynamical systems with symmetry and the mechanisms whereby symmetry can lead to complex dynamics in low dimensional systems (VITA 2005 Other interests: Mathematical education and public attitudes towards...A Java applet for experimenting with kites and darts.
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Java applet to play Penrose tiles Penrose tiles contain only two different kinds of pieces, and they tile a whole plane only nonperiodically. For information about Penrose tiles, read the book Penrose Tiles to Trapdoor Ciphers by Martin Gardner. If you have read Professor Roger Penrose's...Wallpaper patterns and symmetry groups.
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Samantha's Wallpaper Page Samantha's Wallpaper Page Tessellating Wallpaper Patterns (1)New Backgrounds! Tessellating Wallpaper Patterns (2) Non-Tessellating Wallpaper Patterns (1)New Backgrounds! Non-Tessellating Wallpaper Patterns (2) Non-Tessellating Wallpaper Patterns (3) Wallpaper Symmetry Groups Links Blog Sign my guestbook View my guestbook...From the article "One Corona is Enough for the Euclidean Plane" by Doris Schattschneider and Nikolai Dolbilin.
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The Math Forum: Catalog of Isohedral Tilings by Symmetric Polygonal Tiles In the article cited above, tilings* of the Euclidean plane by a single polygon are considered, and it is shown that such a tiling is isohedral if and only if each polygon is surrounded in the same way or, more...Chaim Goodman-Strauss, Arkansas. With interactive demos using Geometer's Sketchpad (requires Macintosh).
http://comp.uark.edu/~cgstraus/
With interactive demos using Geometer's Sketchpad (requires Macintosh).
http://comp.uark.edu/~cgstraus/symmetry.unit/
Pictures of some concrete tilings.
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Interlocking Pavers Molds Make your own truly interlocking* concrete pavers with a high quality polyurethane mold the same durable rubber as skateboard wheels. Properly cared for, these unbreakable molds will retain their value over the years. Surface detail is in the molds. Each...Applying principles of computer graphics to the creation of geometric ornament, as a continuation of the tradition of ornamental design using modern tools and algorithms.
http://www.cs.washington.edu/homes/csk/tile/
Graphics.
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How do you make those pictures? PMG-tessellations How do you make those pictures? How do you make those pictures? P6M-tessellations Back to Hans Kuiper's homepage...Hans Kuiper's work. Tessellations and optical art. Also tessellation software with the 17 wallpaper groups.
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Computer Art, Inspired by M.C. Escher, Victor Vasarely and Sol LeWitt I want to see this page in Dutch Digital Art inspired by M.C. Escher I enjoy to design Figures and Patterns which can be used for Patchwork or Quilting, Textures and Wallpaper drawings. Nice examples are the Donald Duck picture...Tutorials and templates for making tessellations using ClarisWorks, the Geometer's Sketchpad, HyperCard, HyperStudio, and straightedge and compass, including step-by-step instructions for classroom activities.
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Math Forum: Tessellation Tutorials by Suzanne Alejandre Tutorials and templates for making your own tessellations Suzanne Alejandre About This Project||Teacher Comments Student Samples Suzanne's Math Lessons What Is a Tessellation? What Is a Tiling View the MidPoW (March 11 25, 2002 Tiling Triangles Where's the Math? Historical...Links in the Geometry Junkyard.
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The Geometry Junkyard: Penrose Tiling Penrose was not the first to discover aperiodic tilings, but his is probably the most well-known. In its simplest form, it consists of 36- and 72-degree rhombi, with matching rules forcing the rhombi to line up against each other only...Known solutions and a new recipe.
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Pentagons that tile the plane Pentagons that tile the plane The problem here is to find a single tile shape with five sides which can tile an infinite floor without leaving holes. I tried finding new solutions, but I think all the tiles I found...Activities to create patterns using simple resources, such as making equilateral triangle from a circle. Suitable for upper primary and lower secondary ages.
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A collection of activities to help enrich mathematical learning. All use simple materials. Shapes and Patterns made from Paper Circles Geometrical Activities with Magic Paper Making and learning from shapes created simply from “A Paper Window Patterns with Geometrical Shapes...A study for the endless possibilities of tessellating the plane based on the work of Dutch graphic artist M.C. Escher.
http://members.home.nl/wouternimmo
Art of Kenneth Landry. Tessellations, polyhedra and polyhedra decorated with tessellations.
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Landry Art: Tessellations, Prints, and Illustrations This page features art by Seattle artist Kenneth Landry, who specializes in M.C. Esher inspired tessellation- style prints and illustrations. Landry also produces multi-dimensional polyhedra sculptures upon which he often replicates his paintings upon the planar surfaces....Definitions and images.
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Frieze Patterns A frieze is a pattern which repeats in one direction. Friezes are often seen as ornaments in architecture. A mathematical analysis reveals that there are seven different frieze patterns possible. Pattern 1: Translation The only transformation in this pattern is...Compiled by Doris Schattschneider, Moravian College.
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Doris Schattschneider's Bibliography of Tesselations My recommendation for the best introduction to making tessellations is the book Introduction to Tessellations by Britton and Seymour. The comprehensive collection of Escher's drawings of tessellations is in Visions of Symmetry by Schattschneider. There are many articles on tessellations...Software for Macintosh and SGI to create and manipulate tessellations of the sphere, Euclidean plane and hyperbolic plane, and to see how the Platonic solids are related to tessellations.
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KaleidoTile Macintosh is now available at Jeff Weeks web site. For SGI: Download: Triangle Tiling (SGI OpenGL binary) 1.6MB Download: Triangle Tiling (SGI IrisGL binary) 2.1MB Type: SGI binaries These archives contain KaleidoTile, a program based on the Geometry Center's tiling...A program for drawing symmetrical patterns based on any of the 17 wallpaper groups, as well as several frieze and rosette groups.
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Java Kali Home Page Kali is a program that lets you draw symmetrical patterns based on any of the 17 wallpaper groups, as well as several frieze and rosette groups. It was written originally for the Silicon Graphics (SGI) workstations by Nina Amenta. In...Images and descriptions of the 17 plane symmetry groups.
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Wallpaper Groups Click on a pattern to read about it. Table of contentsWelcome! Transformations of the plane Lattices Transformation and symmetry groups The 17 plane symmetry groups each with its own page History References and links Some of these pages are quite...Tilings of Squared Squares and Squared Rectangles, constructed using javascript.
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Squaring.net Tilings of Squares and Rectangles ...Java applet drawing repeated patterns with selected symmetry.
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Escher Web Sketch Sketch takes a while to load, so in the meantime we suggest that you read the documentation below) Location: Switzerland, Mirror: California Pattern Archive The Author's Favorite Patterns The Source Code Download Escher Web Sketch Note: Painting using the images...Tessellation software. 11 rosette, all 7 frieze and all 17 wallpaper groups included.
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Tess Tess will automatically maintain the symmetry group you have chosen; 24 rosette, all 7 frieze, and all 17 wallpaper groups are included. A couple of examples, from our 2002 and 2003 Tess contests, follow. SaffronAlex McDonaldSymmetry Group p3 Triangle CatsSally...Links to activities and other resources.
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Investigating Patterns: Symmetry and Tessellations These links are coordinated with the chapters and activities of Investigating Patterns: Symmetry and Tessellations ACTIVITY 1 (What is Mathematics Title: What is Mathematics? Comment: Observations on the the nature of mathematics from Pathways to School Improvement. Includes Mathematics should...