Bubble Tiles are inspiring some very interesting thinking with extensions in all directions!  As we continue to use them with all ages in our Math Rooms and our partners use them as part of outreach programs, others are looking seriously at the mathematics, developing and documenting ideas for lesson plans, creating apps for the iphone, and making fine art and games for the table top.  Scroll through here to see links to  the works we gathered for an informal meet up over zoom.  In attendance were Lauren Siegel, Austin Bell, John Chase, Tim Reinhardt, Martin Grider, Will Field, Alexander McCluer, and Lauren Sawyer.  If you have interests or ideas about ways to play with Bubble Tiles, please let us know at [email protected] and we’ll invite you next time!

Outreach Events

• The one of each challenge is as popular with the International Congress of Mathematicians as it is with the patrons at the Houston Public Library!  Bubble tiles are proving to be a pillar activity for our math outreach programs whether in facilitated spaces or as part of an unfacilitated activity station.  We have a blog post on just this topic here.

Educator Resources

• Lauren Sawyer, who works for Math Circles of Chicago is the MoMath Rosenthal Prize 2025 winner with a lesson on Bubble Tiles.  She includes some different ways students can generate the tiles with paper folding and analysis as well.

• MathHappens college intern Asa Grumdahl wrote about Heech numbers and bubble tiles in a blog post called The Surounding Game

• This writeup by Nick Rauh, Mathematician in Residence at the Seattle Universal Math Museum is part of their education zone offerings on their website.  Find it here:  https://seattlemathmuseum.org/education-zone-bubble-tiles .

Academic Papers

• High school student Alexander McCluer wrote this analysis in 2024  called The Puzzling “One of Each Tile” Frame that predicts the number of solutions to our ubiquitous “One of Each” Challenge.
• John Chase, Will Field and Alexander McCluer have developed this paper  called Puzzle Pieces and Bubble Tiles and just this week began to circulate the draft for comments and questions among colleagues.  Inside you will find tons of interesting images and ideas!

• To Cut or Not to Cut is a paper by Khushi Pusnur written for Math Circles of Chicago’s QED symposium in December 2025.  It looks at binary operations to define the curve orientation.

Puzzles and Games

• John Chase made a great way to experiment with Bubble Tiles in online form. It is available here on Github.
• Tim Reinhart is a math PhD student in Munich and he is in the final stages of testing an app for iOS. If you’d like a preview seasrch for “Bubble Tiles” in Test Flight. The app has daily puzzles, an informative “About” section, and some wonderful color and graphics options. You can form bubble tiles by clicking on the hexagon walls, and you can see the tiles dissolve into formation above Hokusai’s design as well as do the puzzles and create your own designs.  

• Kate Jones of Kadon Enterprises has done some really interesting pattern finding and making with the “other” Quadrilateral and “pentagonal” Bubble Tiles which, with the triangles make a set we call Bubble 31.  We are looking forward to a formal debut soon!
• Martin Grider of Abstract Puzzle LLC is working on some puzzle and game ideas.  He created a slideshow talk explaining some of the concepts and ideas he considers as he works on playable games.

Origins

• Look in our Bubble Tile Booklet to learn how Bubble Tiles came to be in the summer of 2023
• We told our origin tale and introduced the Bubble 31 (summer 2025) at our MoMath Moves Conference Presentation: Bubble Tile Tale.Here are some images of the Bubble 31 pieces in frames. We realized the potential of symmetry in frames even when restricted to just one of each tile thanks to Kate Jones.  The first 4 frames show creative designs by folks who came by our booth in Philadelphia.  The last 3 frames with all wood pieces contain exactly one of each of the 31 accessory pieces.  Its interesting that the area of the 13 Bubble Tiles we started with is exactly equal to the area of the 31 “Accessory Pieces”.  Counted this way, neither set considers reflected pieces as a seperate piece.

When we add 13 “soft tiles” made by adding one more “side” to a circle by forming a spike, and then another and another and then we mix and match all three sets we get some pretty chaos.

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