Tile or not to tile: Dilemma of Aperiodic Tiling

As a lazy architect, I've always dreamt of designing a non-repeating pattern that could be used repeatedly, showcasing different expressions each time. And lo and behold, a group of researchers, including mathematicians and hobbyists, made a remarkable discovery!

In March, the mathematical world was captivated by the unveiling of the "Einstein" tile—a 13-sided aperiodic mono-tile capable of non-repetitive tiling. But, this tile is not "real" mono-tile since it required mirror translation to fill a plane. The following month, the same group of researchers (they surely love to work overtime) reveal a groundbreaking "real" aperiodic mono-tile called "Spectre" that could tile aperiodically without mirroring. As an architect, this discovery unlocked exciting possibilities for designing aperiodic patterns applicable to various paneling needs, be it floor tiles, facade panels, or curtain walls, using just one type of panel. However, due to its unusual shape, feasibility sometimes becomes questionable, although simplification methods can be found. Back in the 1970s, Roger Penrose, another mathematician (yes, mathematicians seem to encroach on our design territory), discovered Penrose tiling—an aperiodic tiling comprising rhombus-shaped "kites" and "darts." Once again, the tile's uncommon angles posed challenges in construction. But hold on! Around the 1960s, mathematician Hao Wang proposed the Wang tile, an assemblage of 11 colorful rectangular tiles that offered better constructibility. However, it lacked the expressive qualities of the other two. What a dilemma!

Reflecting on these aperiodicity discoveries, it led me to ponder. While it's intriguing to uncover novel ideas, such as aperiodic mono-tiles, applying them to buildings inevitably confronts constructibility issues. Yes, they can still be constructed, but at what cost? Do we truly require these aperiodic patterns in our buildings to the point where we can disregard the expenses? Not to mention the concerns regarding versatility and resiliency of these so-called "Einstein" tiles. Myself, as a researcher and architect, we tend to focus on how we can improve one research or another, and how to incorporate new shapes into buildings. However, sometimes we need to pause and reflect: Is this truly what we NEED?

Well... what a dilemma.