More about the sources and development of this design

by Ian

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Really, this story starts centuries ago with architects and artists in the Middle East who, over the course of many generations, developed an elegant system for creating complex, geometrical designs. That story is largely lost, though. We’ll start, then, with this man, Peter Lu, a physicist, who saw something in the region’s architecture that others couldn’t see.


Here is a classic example of a certain kind of Middle Eastern ornament. It is at the Darb-i Imam shrine is Isfahan, Iran, built in 1453. Peter Lu’s stroke of insight was to look at this dazzling array of shapes and see that it could be broken down into a simple, modular system, one that is only partly related to the shapes you see in the final product.

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Here are the five modules that he identified. He called these shapes “girih” tiles, the persian word for knot, in reference to the strapwork that decorate the faces of the shapes and that end up being the primary design elements. All of the sides of the tiles are equal lengths, all the angles are multiples of 36°, and the strapwork intersects the sides of the tiles (at their midpoint) at 54°. These consistencies allow these shapes to fit together in endless ways, while the strapwork always continues uninterrupted from one tile to the other.

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This insight is astounding because these shapes don’t make up the border of actual tiles, but rather are a system for the layout of these designs. It’s not as if Peter Lu looked closely and saw the grout lines of tiles that no one else had noticed. Rather, he saw that the designs could be achieved by linking their repeating, strapwork elements to other, unrelated shapes, and that these shapes could then be used to map out the designs in countless ways over any surface. In the picture above you can see how the design is comprised solely of the strapwork, but how this strapwork can be arranged using the “girih” tiles.

All of the images in this post to this point have come from a cool article, “The Tiles of Infinity,” about Peter Lu and the “girih” tiles, which you can read here.

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It is not incidental that Peter Lu is a physicist. There is a branch of physics, for reasons that I don’t claim to understand, that is devoted to tiling (ways in which shapes can fit together to fill a plane). In the 1970’s, physicist Roger Penrose developed a system of tiling, now known as Penrose tiles, whereby two shapes can fit together to fill an infinitely large plane without ever repeating. It was thought to be the first such system. Now it is believed that the “girih” tiles, developed at least 500 years earlier, can also do this.

The “girih” and Penrose tiles share other similarities, too. They can both be arranged with five-fold rotational symmetry (“girih” can also have ten-fold), meaning it will look the same when spun 72° (or any multiple thereof). Just looking at two clusters of tiles, above, you can tell that they are related at some level. The picture on the left is a grouping of “girih” tiles, while on the right are Penrose tiles.

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Do a web search for “girih” and you will find plenty of people playing around with the fruits of Peter Lu’s labor (and, let’s not forget, the labor of countless forgotten artists from the Middle East).

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Computer aided drafting and the laser cutter are a powerful update to the work that once took who knows how long with compass and straightedge.

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Del Harrow, a ceramic artist whose work I admire, has also worked with these shapes. His use of the “girih” strapwork pattern is very direct, yet he has managed to make pieces that are unique and modern looking.


So, you can see, this is not new territory. Since Peter Lu decoded the structure of the historical “girih” patterns in 2007, plenty of people before me have been exploring these same shapes and patterns. If the design for this tile installation is innovative, it is in the creation of a topography for each tile that is made up of triangular facets, which is easy to see in the picture above. All of the lines of the “girih” tiles remain, incorporated into a slightly more dynamic geometry.


Triangular facets inevitably give something a more contemporary look. They seem to be a ubiquitous feature in the architecture and design of our time.

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I think triangular facets have such a current feel because they are the signature of design done with 3-d modeling software. It is how a computer makes a curved surface. If you put tons of information into that surface, it can look seamless, but with less information it must be broken down into larger and larger triangles. These sexy vessels by Phil Cuttance are a good example. I don’t have any idea how they were designed, but they have the look of a flowing surface starved of enough data points.


That’s not how I arrived at these shapes. As I often do, I started by carving on chunks of plaster. The design and these scale models were born at the same time.


In short, this is a highly derivative design. I don’t think that’s necessarily a bad thing. In this case the sources of derivation are deep and time-tested. I just wouldn’t want anyone to think that I conjured this design out of thin air. At best, I hope it will be seen as a contemporary riff on some timeless forms and gestures.

Meanwhile, Andrew and I have a lot more finished product. We’re also developing the color scheme for the glazed tiles that make up the kitchen side of the wall. More pictures are coming soon!