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The Mathematical Art of
 David A. Reimann
drMathArt in LEGO (Artwork)
drMathArt in LEGO lego 2021

The text dr Math Art rendered with Truchet tiles made from lego. The backing plate contains 64x64 studs.

Background and Inspiration

In this piece I revisit an idea of mine I wrote about for the 2009 Bridges conference on creating text from Truchet tiles. That earlier work was purely digital, but I recently realized these tiles could be created using lego.

A Truchet tiling uses a square tiling where two quarter circle arcs connect pairs of adjacent sides of each square. Because the arcs are continuous across the boundary, the arcs form continuous paths. Furthermore, because the first derivative of the curves is continuous across the tiles, there are no sharp corners. The resulting Truchet pattern is a collection of meandering paths.

After looking at random Truchet patterns I noticed there where times when shapes that looked like letters appear. That was the focus of my Bridges 2009 paper. George Hart, then Chief of Content at the National Museum of Mathematics (MoMath) in New York, contacted me about using this idea at MoMath. Custom tiles were made and used to create decorative Truchet tiling patternss in the museum bathrooms. Each tiling pattern contained a hidden message.

Truchet Tiling patterns at MoMath located in the men's (left) and women's (right) restrooms on the first (top) and lower (bottom) levels.
Closeup of Truchet Tiling pattern at MoMath showing scale of tiles.

In 2020, I discovered that Truchet tiles could be constructed using lego 2x2 macaroni bricks (ID 3063) and tiles (ID 27925). This would presumably work with 4x4 sizes as well, but I have not tried. The 2x2 pieces require a 3x3 field.

Truchet tile in lego can me made from macaroni brick or tile pieces (left). Each tile is placed on a 3x3 field (right).

A combination of lego brick and tile pieces can be used to enhance the text as seen in this work. The bricks can be topped with tiles as well. Lego has limited baseplate colors and sizes, however Strictly Briks makes 32x32 baseplates in many colors. The artwork here uses four 32x32 baseplates.

The Museum of Math has used Truchet tiles for a number of fun activities in recent years. Knowing that these tiles can be easily made with lego pieces might inspire others!

References