Tiling Tools and Apps

• Truchet Tiling

  • http://www.cr31.co.uk/stagecast/wang/stage.html

• Penrose Tiling

  • https://craftdesignonline.com/penrose

• Girih Tiling

  • https://girihdesigner.com/

Tiling Apps

• Truchet Tiling: https://dmackinnon1.github.io/truchet/

• Wang Tiling: https://www.boristhebrave.com/permanent/24/06/cr31/stagecast/wang/stage.html#

• Penrose Tiling: http://craftdesignonline.com/penrose/

• Girih Tiling: http://girihdesigner.com/

References/Bibliography

• Truchet Tiling (wikipedia)

  • https://mathworld.wolfram.com/TruchetTiling.html

  • https://momath.org/home/math-monday-truchet-tiles/

  • https://chalkdustmagazine.com/features/too-good-to-be-truchet/

  • https://boardgamegeek.com/geeklist/54579/games-inspired-truchet-tiles

  • https://www.instructables.com/A-Maze-ing-Fun-with-Truchet-Tiles/

  • Bridges papers on Truchet tiling

    • Play Truchet: Using the Truchet Tiling to Engage the Public with Mathematics, Cindy Lawrence, National Museum of Mathematics, New York, NY, USA, http://archive.bridgesmathart.org/2018/bridges2018-359.pdf

    • Infinitely Variable Tiling Patterns: From Truchet to Sol LeWitt Revisited, Robert J. Krawczyk, http://bitartworks.com/paths01/Patterns_2020.pdf

    • Multi-Scale Truchet Patterns, Christopher Carlson, Wolfram Research, Champaign, Illinois, USA,  https://archive.bridgesmathart.org/2018/bridges2018-39.pdf

      • https://github.com/ciaron/multiscale-truchet - project implementing Multi-scale Truchet Patterns

• Wang Tiling (wikipedia)

  • Wang Tiles, Introduction, https://www.boristhebrave.com/permanent/24/06/cr31/stagecast/wang/intro.html

• Girih Tiling (wikipedia)

  • The Tiles of Infinity, Sebastian R Prange, Aramco World, Volume 60 Number 5, https://archive.aramcoworld.com/issue/200905/the.tiles.of.infinity.htm

• Penrose Tiling (wikipedia)

• The Hat, a solution to the "einstein" problem (wikipedia)

  • An Aperiodic Monotile - academic paper describing the Hat

  • The Einstein Mad Hat awards, from the Museum of Math, entries by October 15, 2023

• Frieze Groups

  • Frieze Pattern Explorer

• Wallpaper Groups

  • Wallpaper Pattern Explorer 

• Grid Paper

  • Grid Generators

  • 1cm Triangular Grid

  • 5mm Square Grid

• Frieze Pattern Explorer 

  • - David J. Eck, Demo for Math 110: Discovering in Mathematics

• Wallpaper Pattern Explorer 

  • -  David J. Eck, Demo for Math 110: Discovering in Mathematics

• Eschersket.ch

  • Symmetry design tool/app, prettier than The Wallpaper Explorer!

  • Particularly fun for Rosettes (rotational symmetry)

  • Can download SVG format which can be useful for digital fabrication.

• KaleidoPaint

  • iOS tessellation app

  • only Image download

• 3dp.rocks/lithophane/ 

  • Image to Lithophane - Texture Roller (When set for Solid Cylinder)

• Ashlar,  Download Whole Pattern:

  • Click the "Export as SVG" button to download a large section of the repeating pattern. 

  • Convert the SVG format to an easier to use format like Adobe Illustrator with an online conversion tool.

  • Import the .ai file into another design software for editing and/or printing.  

  • Possible applications:  

    • Laser Cut paper stencils for Slip resist

    • Laser-Etched design tiles for pressing into clay, or for use on their own

    • Input for curve-based geometry in Rhino or another 3D Modeling software.

  • Ashlar, on Github (code-sharing platform)

• Orbifold Notation (wikipedia) for symmetry groups

  • From the book

  • The Symmetry of a Tiling, Brian Wichmann and Tony Lee

• Rhino/Grasshopper Plugins

  • Parakeet

  • Orbi

  • Symmetry Arrow

• Ashlar

  • Goto the Ashlar tile design app

  • Use the Editor window to change the edge profile. 

  • Try out different tessellation patterns in the "Tiling Type" Menu

  • modify Scale to get a good preview of it as part of a large and small array.

  • Things to watch out for a clay tile cutter 

    • avoid tiny details

    • avoid sharp, thin parts

  • Save the Base Tile:  Right Click on the single Tile Preview, "Save Image As..."  and give it a distinctive name.

• Cookie Cad

  • Sign in or create a login

  • Import the single Tile Preview

  • Recommended Settings

    • Size: 100mm - 125mm (4-5 inches)

    • Height: 16mm (.63 inches)

    • Thickness: 1.5mm ( thin)

  • Download your 3D file

• Printing

  • KCAI Beals Studio Resources

  • Set Print Fill to 75%.  This will make the cookie cutter solid, rather than double walled with a bit of infill.

  • Prints will take about 1 hour each, and may not be able to fit together. 

  • Clean the brim off the bottom edge after printing.  

• Use

  • Get a small pile of Corn starch 

  • Dip the tile cutter in Corn Starch, like you would use flour with a cookie cutter

  • Press the Cutter down uniformly.  A small ware board on top does this nicely

• J H Conway, H Burgiel and C Goodman-Strauss. The symmetries of things. A K Peters Ltd. 2008. ISBN 978 1 56881 220 5

• B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman & Co., New York, NY, 1987. 

• K. Critchlow. Islamic Patterns: An Analytical and Cosmological Approach,  Inner Traditions, Rochester, VT, 1999. ISBN 9780892818037

• Tiling Database, Brian Wichmann and Tony Lee, http://tilingsearch.org/index1.htm

• Generalizations of Truchet Tiles, K Mitchell, Bridges 2020 Conference Proceedings, 2020, https://archive.bridgesmathart.org/2020/bridges2020-191.pdf