Cecil Balmond has some fantastic work in his books (A+U, Informal) regarding his use of fractals for a tiling pattern in a Liebskind project. This project uses an aperiodic fractal tiling pattern. An interesting lexicon here is that that the word “tiling” means not only the “physical laying of tiles” but is a mathematical term for the mathematics of tessellations. While this idea has been found in ancient Islamic ornamentation, this is the most recent use of that I know of.
This project uses a particular tiling pattern called Amman tiling with dimensions that are all related by the ratio 1.618 (golden proportion). As you can see in the facade (best image I could find) the Amman tiling pattern is used at several scales so that the fractal pattern would be (it’s not built) more evident as you approach it…theoretically infinite resolution.
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