Geometry in Five-Dimensions: Building Quasicrystals from Penrose Tiling

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Geometry in Five-Dimensions: Building Quasicrystals from Penrose Tiling

Deborah Coombs

Duane Bailey

Art

No-one really knows what quasicrystals look like. But we do know, from the diffraction patterns of X-ray crystallography, that they bear a resemblance to Penrose tiling. By combining artistic exploration with mathematical insight into the five-dimensional nature of Penrose tiling we have begun to visualize the structure of quasicrystals.

We are building mathematically precise sculptures of Penrose tiling raised up to a dimension of somewhere between 2 and 5. We have also devised algorithms to explore two-dimensional aperiodic tilings using color and perspective. These drawings sometimes reveal structural patterns that become sculptures.

In January we built a mirrored glass and copper sculpture that attempts to reconstruct the crystallographic origins of Nobel prize winner Dany Schectman’s famous five-fold diffraction patterns.

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