PLIX Beautiful Symmetry: Reflections from the Co-Design Process

As of this week, the PLIX team has begun its second activity co-design sprint, teaming up public librarians with an MIT Media Lab researcher to generate new creative learning programming for the library setting!

Throughout November and December, we are partnering with @JeanSlavkovsky (Malden Public Library, Massachusetts) and @claudiahaines (Homer Public Library, Alaska) to co-create a new activity based on the work of Alex Berke, a Ph.D. student at the Media Lab (City Science group). Alex’s research spans the domains of computer science and software engineering, data science and machine learning, and the development of distributed systems. The work we’ll be focusing on, though, is a coloring book that Alex published which aims to spark a hands-on and creative way to learn about mathematics through an exploration of symmetry! :crayon:

In this thread, we’ll be sharing reflections as we develop the new PLIX Inflatables activity, design learning prompts, create a new zine, and more, as a form of open documentation of the co-design process. We hope that you’ll share new ideas, ask questions, and leave comments and feedback along the way!

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At the library, I often design learning experiences that provide entry points for kids, particularly littles, to explore ideas for the first time or in a different way. Our first week of co-design got me dreaming about how children think about abstract concepts like symmetry. As Alex introduced her coloring book and perspective on symmetry learning, I immediately turned to the natural world that helps define life in my small coastal community. How can we draw attention to the different kinds of symmetry children and their families, wherever they live, may already see around them but not know how to name or manipulate? What play-based activities can we design to inspire exploration into this cool math concept?
I cut and played with paper blocks to recreate Alex’s examples of translation, mirror and glide symmetry as we talked about pinwheels, bird wings, bicycle wheels, and flip books. Using multiple senses to explore the concepts we were talking about got my creative juices flowing!

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It was great to get the story behind the project and the terminology last week from Alex. The idea of showing the process of creating the symmetries through animation was an idea I really liked. The wallpaper generator on the Beautiful Symmetry website was soothing but also made the rotations clear. I hope somewhere in the process, I can play around with frame animations from pictures or motion graphics because I think it would help as a supplemental resource. It will be interesting to start to use different media (ie stamps, coloring, paper-cut) to show the same concept.

During play testing, I experimented through cut paper and making stencils to color in a pattern. Coloring it in definitely took more time than cutting, but coloring helped me see the process more because I was manually rotating the stencil.

My attempt at making a negative space stencil:

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Beginning the design process has been a wealth of possibilities. Thankfully, we have Alex Berke’s beautiful coloring book as a centerpiece:

Alex also designed a mini workbook that reviews the types of symmetries we’ll be focusing on:

And the PLIX team provided a kit to get the creativity going:

As an adult services librarian, I have witnessed the popularity of coloring grow from a predominantly children’s activity to an activity appreciated by all age groups, particularly for it’s meditative qualities. Coloring pages create a fenced in playground for creativity, a framework that can make being creative less daunting. For this activity we are using that framework to teach mathematics, while allowing space for discovery and experimentation.

I began by familiarizing myself with the basic concepts of symmetry outlined in the coloring packet (Translation, Mirror Reflection, and Glide symmetries) by doing the exercises myself:




Through doing these exercises, I began to recognize patterns of symmetry in other aspects of life, especially in music. What struck me most was the importance of breaking patterns and how setting a pattern and then breaking it captures our attention in a new way.

When coloring, we often naturally create and break patterns to create something we think is beautiful; by introducing the discussion of mathematical concepts, we are defining what already exists. Another aspect of the design process is determining how much new vocabulary to introduce. There needs to be enough to be able to discuss the concepts, but no so much to deter the audience from the activity.

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Hi, all! Reporting out from last week!

Echoing some of the thoughts from my fellow co-designers, I am so excited by the many directions in which this activity might grow. In doing some preliminary research (and through reading the introduction of Alex’s book), I’ve come to realize the role of symmetry in most things around us: nature and biology; art and architecture; textiles; poetry, language, and literature; music. In our playtest last week, @claudiahaines mentioned that she would love for her patrons to notice or discover “symmetry where they are” – my hope is that we can create a series of activity prompts that potentiates this process of discovery, creation, or simply “noticing.”

With this in mind, I’m starting to think about the different ways in which to engage symmetry: how do we understand what symmetry means? Through creating patterns, and then destroying them? Through found objects, and through photography? Alex’s Beautiful Symmetry encourages understanding through coloring, and I am wondering how we can carry that idea forward into other realms of creativity. Some thoughts from my initial brainstorm:

To highlight one discussion point from our playtest last week: we’ve been tasked with thinking about ways to integrate the terminology or nomenclature of different symmetry patterns (translation; glide and mirror reflections; rotations) into the activity we’re working towards. Typically, in PLIX activities, we try to avoid too much technical jargon, but knew that this nomenclature was something we’d like to incporproate into the learning and material design. We’ve begun to think about various ‘tools’ that facilitators or patrons can create to help understand what these terms mean. I thought about creating a ‘symmetry toolkit’ with various easy-to-make objects that help in identifying what type of symmetry an object or drawing contains.

Also, Alex has led online workshops in which participants use the Zoom annotation feature to collaboratively color pages from the book in a virtual setting! We got to try it out!

Would be curious to hear about how and when folks see symmetry around them as they go about their day! Looking forward to continuing this process of discovery over the next several weeks : )

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I tried a few ways to make wallpaper and border/frieze patterns.
One was an asymmetrical stencil (Cara did something similar above with a symmetrical one) traveling along a ruler. I could imagine a variety of asymmetrical shapes cut our of heavy card or vinyl which patrons could color or sponge paint through.

Then I wondered if you had a deck of transparent “cards” (like overhead projector prints: toner on acetate) all with the same fundamental asymmetrical shape that you could lay out and play with the variations in rotation and translation, and see how many different permutations you could get from that shape, that could be cool! Here’s a quick sketch with a very irregular shape which is trying to be the 4-arc shape from the screenshot in Avery’s post.

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I absolutely love the coloring book! I have often worked with tessellations with older kids. Although it it can be a challenge for some perceptually. Also, we have done the flexagon project several times and, although also challenging, it can produce great results. (https://www.auntannie.com/Geometric/HexaHexaFlexagon/)
For youngers I love tangrams as a great way into symmetries and geometry, and there are a few nice little books, like Tangram Cat.
This also leads nicely into origami paper folding, which is always a hit at our learning center as an independent activity, or incorporated into workshops for other topics. I think it helps to improve spatial awareness, fine motor skills, and patience :slight_smile:

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My retweet of a popular tweet on twitter sparked a fascinating reply that reminded me of this PLIX beautiful symmetry project.
The sound waves produced by the vibrations/resonance of different frequencies create beautiful, symmetrical patterns with sand:



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Oh this is so cool! I was trying to figure out an activity involving symmetry in music that doesn’t assume the ability to read music, and this is an angle I hadn’t considered. Thanks!

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Beautiful Symmetry Week 2

During the second week of co-design we began the process of taking what we learning about symmetry and the Beautiful Symmetry coloring book and turning it into a creative learning process.

I discovered that designing a creative learning activity has many challenges:

  • How much information do we provide/is necessary to start the activity?
  • How do we minimize how much the facilitator need to know before offering the activity?
  • How do we create an activity with the same starting point that results in a diversity of outcomes? (How do we create low floors, high ceilings, and wide walls?)
  • And it should be fun!

To help us figure out the above, we are trying out a bunch of activities that encourage playing with symmetry. I’m working on a bead bracelet to illustrate wallpaper patterns, and cutting snowflakes which I think will illustrate a variety of symmetries, particularly glide reflections. We shall see!

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Exploring Symmetry in Nature, and Using Nature to Create Symmetry

Last week, I took to the outdoors to hunt for symmetry in the world around me! Something our co-design group has discussed (and an idea we are working to incorporate into the Beautiful Symmetry learning activities) is the process of uncovering symmetry in the natural world, recognizing the ways it emerges; how it presents itself, lends function and form; enables process. I spend a lot of time thinking about–and immersing myself in–the natural world, but not necessarily with an eye towards identifying patterns of symmetry within it! I took advantage of a local pollinator garden while on break in New Hampshire last week, and took some photographs of what I found most compelling (symmetrically speaking!). Here are a few of my findings:

Just by thinking consciously about symmetry in nature, I was better equipped to notice patterns (or lack thereof) emerging around me. I have since been brainstorming ways to take this process further–specifically thinking about how to shift the process from one of discovery towards one of creation. In my research, I came across some work by artist Anni Albers. Albers was a weaver, but arrived to the United States without a loom. Improvising, she began to “sketch” weavings and tapestries using natural materials (and encouraging her students to do the same), exploring how horizontal and vertical textures were crafted by different (and incidentally, often symmetrical) arrangements. Below are two examples using corn kernels and woven grass:

Moving forward, I’m planning to re-enter the field, this time collecting materials that I can use to emulate this ‘weaving’ symmetry with nature protocol. I am excited to explore how I can use symmetrical pieces to explore different types of turns, glides, and reflections! More to come!

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Over the past week, I’ve been exploring symmetry with potato stamping. After drying them out a little, I started cutting them into 1" shapes to fit the worksheet. To try to minimize the messiness, I stuck push pins in them so they would be easier to grab. The stamping was imperfect but I liked the overlaying of colors and textures!


(mirror reflection on x- and y-axis)


(mirror reflection on x- and y-axis)


(1/6 turns)


(translation on x-axis and mirror reflection on y-axis)

I played around with different kinds of symmetry on the grid paper. I like the way the mirror reflection on the x- and y-axis came out and it was really exciting to see the wallpaper pattern come together.

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Update on Prompt Brainstorming!

Over the past month or so, the BeauSymm co-design team has explored multiple paths for learning both with and about symmetry. Last week, we were able to distillate our independent findings (AKA creations!) into a series of prompts that we think could engage a wide variety of patron interests (as well as learners of all ages, including adults). On the team, we are fortunate to have both a youth services and adult services librarian, with @claudiahaines and @JeanSlavkovsky both lending their particular expertise in understanding what type of workshops/activities–and how they are framed–work for the age group they primarily work with.

We are envisioning Beautiful Symmetry as a series of activities: a choose-your-own-adventure for immersing yourself in the ideas of mathematical symmetry and the ways it might be used. In this format, the program as a whole could exist as a series of activities, a drop-in workshop, a collaborative installation in the library, or a one-off event. Here are some prompts we came up with:

  • :yarn: Design a textile or wallpaper pattern using customized stamps
  • :infinity: Explore infinity by cylinder seals
  • :ledger: Craft a flipbook to animate symmetrical images in motion
  • :memo: Make an algorithm, in Scratch or on paper, that leads to art based on symmetry
  • :four_leaf_clover: Explore the natural world to capture imagery of the way symmetry lends form and function
  • :chestnut: Build a sculpture or tapestry using symmetrical elements found in the ecosystem
  • :honeybee: Design a dance with symmetry-inspired choreography to tell a story or send a message
  • :crayon: Destroy or remix symmetry using color through a collaborative installation

We are planning to further investigate these prompts for the level to which they can be embedded with the values and ideas of creative learning. In particular, we are interested in maintaining high ceilings for these activities, meaning that there is a ton of potential for a leaner to engage with the ideas and create sophisticated projects for a given prompt. An additional consideration, raised by @JeanSlavkovsky, is the necessity to have leaners start from common ground before embarking on the many potential ways to create with symmetry (this idea ties into the low floors dimension of learning, meaning that it’s easy to get started with a project). For this, we are discussing use of Alex’s original coloring book (or perhaps simply coloring to make or break symmetry) as a starting point.

One other great idea that @claudiahaines had was to divide the various prompts into core themes that we’ve discussed in the past (e.g., symmetry as art; symmetry as structure; symmetry as purpose), which will make it easier for librarians to decide which activities to run, and more easily tailor them to patron interests.

If anyone has any initial thoughts on the prompts that our co-design team devised, I would love to hear your input! Which excite you most? Which seem confusing or difficult? Are there other forms of engagement or creation that we should be thinking about?

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I don’t often have the opportunity at the library to do this level of design work over such an extended time period, so our BeauSymm group’s process is refreshingly fun. During the co-design discussions last week, we moved from own exploration of the concepts to creating replicable activities and the ZINE. I’ve already played with the idea of a flipbook, so I’ve been thinking about paper play for a couple of weeks. I’ve also been looking at the Space Food zine, among others, recently for an upcoming virtual “Scene by Scene Zines for Teens” program I am hosting. As I played, I got to thinking about not just the information and the convenient folded aspect of the zine, but how the backside of the zine - often left blank - could be used in a creative way. As a group we tossed around the idea of sharing information on the one side, similar to the folded Space Food and Paper Circuits zines that the Media Lab has created, but also including a “your turn” interactive space on the other side. Maybe the designs (colored?) could even be represented infinitely if the zine is folded into a sphere like the Tlingit basket pictured in this post? Or the individual designs could be joined with others in an in-person program to create a bigger collaborative design? Just some thoughts. If we’ve inspired any ideas in your head or you’ve seen something along these lines, let us know!

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As Avery mentioned, I am an adult services librarian. Trying to design STEAM activities for adults seems to be as much in the advertising as in the activity itself. Like children, many adults love coloring and crafting, so Beautiful Symmetry is a perfect fit, but the challenge is coming up with a universal name for the zine that appeals to all ages, as well as the creation of the content of the zine.

My hope is to hold this activity in many forms for various audiences, engaging adults in a family setting and an adults-only setting. For all programs, coloring is a natural starting point; it is how we learned the principles of symmetry for designing this activity and our patrons can benefit likewise. For the adults-only version, I plan to use different activities or use different materials than I would for a program involving younger children. Most of the activities we discussed can be scaled for complexity and tailored to various palettes. The rolling stamp activity @caratarmey explored can be as simple as adhering foam stickers to a stuffed toilet paper roll, or you can modify a rolling pin and create intricate designs using string, customized rubber, carving etc.

Creating snowflakes can be as simple as cutting them out, or as complicated as programming the design. Some patrons, of any age, will be more comfortable on a computer than with scissors in hand.

This activity is very broad and customizable, there can be many ways to make the “same thing” (i.e. snowflake), but many ways to get there and many outcomes. The zine we are designing needs to lay groundwork to get anyone started with endless possibilities.

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Last week, we discussed the zine more and how to start the process of compiling all we’ve learned/experimented/considered. As @claudiahaines mentioned above, activating the space on the back of the zine could help the ideas of symmetry come to life. There are many different routes we can take to use the back. As we experimented with last week, the way the zine folds makes for interesting 3D shapes and possibilities. The natural folds also could play into ideas of mirror symmetry where you could make only see one side at a time by folding it over. I’m still playing around with those, but at the very least we can put a grid on the back so it becomes like worksheet starting point.

We also discussed the potential content of the zine and a possible character to guide us through. We discussed the idea of a bee being the character because of how they interact with symmetry all the time. From @JeanSlavkovsky’s research: their honeycombs have symmetry, they are attracted to symmetrical flowers, their waggle dance has symmetrical moves, etc.

I started looking at bees and how to make them into a character:

And then I started to sketch some (making them more on the realistic side but still friendly):

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Exploring BeauSymm remixes: symmetry in digital interfaces

This week, @binka and I met with Media Lab researcher Nina Lutz to think about some ways to explore symmetry using digital tools. Nina uses javascript to create works of art through writing code (she posts daily work to her Twitter feed–check it out!); we thought we might be able to implement a component of the BeauSymm activity that extends into the coding-to-create realm through free and easy-to-use online tools. (There’s also a deep, rich history of creative computation rooted in the Media Lab, and so it’s an additional tie-in for connecting research there to our public library programming!) Nina’s works are created using p5.js, an online tool for creative computing that’s also home to a community of creators who remix (or ‘fork’) the work of their peers. The tool is free to use, and requires no downloading–think of Scratch, but with Javascript! The p5.js editor allows you to easily remix code, as well as visualize what you’re code creates in real-time. Here’s an example:

(If you’d like to try out the p5.js editor, but are unsure of where to start, Nina put together a wonderful tutorial that guides you through creating examples and provides tips for starting and remixing sketches.)

We used Open Processing to identify interesting programs that were tagged with or incorporated an element of symmetry! In my searches, I found a few that I loved :smiley:(I’ve included links to the source code along with each image–feel free to try out pasting that code into the p5.js editor to take on your own forking!)


DeepSeaRhizome, by jby


Line Abstract, by Richard Bourne

p5.js can seem a little bit intimidating (it was–and is, but I’m learning!–for me), and so I also wanted to see if I could use a more familiar tool for visual coding symmetry: Scratch! The Scratch community has also created a ton of projects that rely on symmetry to create interesting and beautiful visuals (and are easily remixable! You can take a look through these results to find some you love). I rather liked this one, which looks a lot like the first example I tried out in javascript!


Rational Symmetry, by junebeetle

@claudiahaines also mentioned the idea using Google sheets to build out symmetries in a collaborative manner, inspired by workshops she’d previously run where the theme was to create 8-bit-like digital art. This way, the projects would not only be collaborative (multiple patrons could work on the same sheet at a time), but would also be easy to get started with (low floor), and would prepare patrons to begin thinking about how they might use more sophisticated tools like Scratch or p5.js moving forward. @katherine and @JeanSlavkovsky also noted that knitters use spreadsheets to plan their patterns and designs, which is a wonderful tie-in to the textiles prompt we previously described!

We’re still thinking about how to incorporate these digital tool and interfaces into the project–likely as a BeauSymm Remix–, and we are doing more research to investigate what resources exist in this domain already (would love ideas if anyone has them!). Stay tuned!

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Wrapping Up Co-Design and Looking Forward!

Last week, we wrapped up the final chapter of our co-design sprint for Beautiful Symmetry! Over the past six or so weeks, @claudiahaines and @JeanSlavkovsky have helped the PLIX team brainstorm a wide range of prompts through which to engage symmetry creatively and in an open-ended manner, and helped to set the stage for a brand new PLIX zine! We’ll continue to work on those resources (including an in-depth activity write-up) and share them out early in the New Year!

I hope to keep this thread going as both the co-design team as well as the broader PLIX community has new ideas, thoughts, or questions about this new activity. Keep an eye out for information regarding BeauSymm beta-testing, too!

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This practice of watching where our Intention takes our Attention could be an interesting mental health lesson to add to this STEAM project. When we begin to focus on a particular thing/topic/idea, it seems like the world is suddenly filled with that subject- nature, radio ads, book references. So, if we decide to look for evidence of symmetry in nature, we will probably find it. If we decide to look for positive things in life, then we see it everywhere. Of course the same thing goes for negativity and judgement.

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The simple act of keeping a beat while others around you have separate beats is symmetry. How some instruments echo or reply to others in works would be the same thing. Booms whackers would work really well for something like this… hmmmmm… I wonder?

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