Path to the Garden

About a year ago, I was lucky to have attended Ingrid’s and Dominique’s presentation at the JMM where they introduced their proposal for Mathemalchemy. I immediately offered my support, but admitted that I did not feel qualified to join the group. After all, I am a mathematician, not an artist. Dominique assured me that I’d be welcome, but I remained uncertain. I even drafted an email later that night thanking her for the opportunity, but assuring her that she was mistaken to allow me to join this team. Thankfully, I hit delete instead of send!

First maquette presented at the JMM 2019
First maquette of Mathemalchemy presented at the JMM 2019.
Samantha tiling her bathroom.
Me, tiling my bathroom.

Fast forward a few months later to our first official (virtual) workshop. I was eager, but still unsure how I could contribute. Nevertheless, I joined the Garden Group and we began brainstorming ideas. I suggested that the garden should have a path, and Li-Mei had the fabulous idea that the path should be formed by a Sieve of Eratosthenes for the Gaussian integers. Immediately, I envisioned these stepping stones as mosaics made from tiny square tiles. And then I realized – “Hey, I can do that!” Having recently learned how to tile and grout while remodeling my bathroom, I confidently volunteered to take on the construction of the garden path!

The question now became – how can we ensure that the mathematical concept is clear? This took several attempts and many back-and-forth discussions. With COVID-19 restrictions, shopping for materials in person was not an option. I picked out some colored tiles from an online shop and hoped for the best! Unfortunately, after making the first set of tiles, it became clear that the tile and grout colors did not provide enough contrast to make the patterns distinguishable. However, it gave us a proof of concept and a direction to move forward!

First set of tiles made clear that the tile and grout colors did not provide enough contrast to make the patterns distinguishable.

We decided to replace the beige tile with a bright white tile and darken the grout color to provide the desired contrast. Additionally, inverting the light and dark colors allowed the white tiles to shine on a predominantly brown path, highlighting each Gaussian integer multiple as it arises in the sequence. 

Garden path options
Different options of tiling for the path.
63 tiles “washed away” by the rising and falling tide.

After settling on the design, fabrication was the final step. Unfortunately, we had one final obstacle to overcome – inverting the brown and white tiles left us precisely 63 brown tiles short. Although we likely had enough time to order more (naturally, they were out of stock!), I saw this as an opportunity to get a little creative. The path through the garden leads into our bayside coastal scene. What if the last stepping stone was weathered, having been washed away by the rising and falling tide? I created a prototype and Dominique loved the idea. Our garden path was officially complete!

Looking back on this year (as we all tend to do on New Year’s Eve), I am thankful that my path brought me to our “garden of mathematical delights.” I am thankful that I learned how to tile my bathroom five years ago, and I am especially thankful that I never sent that email to Dominique!

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