3D QR Codes

Summary

3D QR Codes Erik Demaine & Martin Demaine, 2025 In this exhibit, we're experimenting with the limits of QR (Quick Response) codes, in particular new ways to construct QR codes from physical material. Most of our QR codes are built from several layers of material (wood, paper, or acrylic), where each layer is a single color. Building in this way has an interesting constraint: each layer must be a connected piece of material. We use a greedy algorithm to find the most white pixels that can appear in the top layer, then find the most black pixels that can appear in the second layer (while also including pixels from higher layers, to maximize connectivity), and so on. This algorithm is guaranteed to decompose the QR code into the optimal number of layers. (If we had three different colors instead of two, the problem becomes NP-complete, meaning that there is probably no efficient algorithm to optimize the layers.) Surprisingly, most QR codes require only four layers to build in this way. In one piece, we show the individual layers in addition to the stack. If you want to try your own messages as multilayered QR codes, try out our open-source software! Most of our QR codes use a feature of the QR specification that “black” versus “white” pixels are determined by brightness, or more technically, reflectance — the amount of reflected light. A pixel is considered black if it has less reflectance than midway between the maximum and minimum reflectance in the image, and otherwise it is considered white. This lets us use dark and light wood to represent black and white. We can also use a mix of colors: our paper QR codes use a different color for each layer, alternating between light and dark colors. Layered Paper QR Codes [P0201] “This Is Fine” (2025), Mi-Teintes paper, 11" × 11": [P0202] “What's Your Favorite Color?” (2025), Mi-Teintes paper, 11" × 11": [P0203] “The Light and Dark Sides of the Moon” (2025), Mi-Teintes paper, 11" × 11": [P0204] “What Is the Color of Love?” (2...