Written by: Veronica Ilkow & Mateen Wagiet
Thursday, 8th February saw the Arcade at Bush House come alive, where a gathering of student structural biologists and crystallographers, under the guidance of Prof Brian Sutton (from the Asthma & Allergy Sub-group within the Randall Centre), to build the world’s first and largest non-periodic tiled pattern one tile at a time.
A collaboration with artist Dr Shelley James explored the colourful tiling patterns of the 13th century Alhambra, and examined the 21st century discovery of quasiperiodic lattices whilst applying the ground-breaking discovery of left- and right-handed crystals by scientist and printmaker Louis Pasteur. The event, hosted by @CulturalKings drew over 100 people, many of whom actively participated in a drop-in creative workshop conducted by Dr James, where participants were able to create and add their own left, or right-handed tile to a giant quasi-periodic pattern (check out the red and blue tiles).
Figure 1: Dr Shelley James demonstrating the process of printing individual left and right- handed tiles which are mirror images of each other.
Figure 2: Participants were introduced to a form of ‘forbidden-symmetry’. The public received a hands-on opportunity to build, with the use of Penrose tiling, a 5-fold symmetrical pattern, otherwise not seen in nature. Participants had to follow local matching rules, where yellow spots had to be paired with yellow spots while orange spots could only be aligned with orange spots. Participants were shown the beauty of local symmetrical pattern creation; whereby the global pattern is best described as not only infinite, but also that the arrangement of the tiles do not repeat.
Figure 3: Prof Brian Sutton, explaining how any 2D planar pattern can be divided into only 17 groups describing the underlying symmetry of the pattern.
Roger Penrose who discovered Penrose tiling said that he did not think it was possible to create a non-periodic pattern with less than two tiles. The amateur mathematician Joan Taylor solved equations proving that it was possible but could not confirm that such a pattern could be built one tile at a time. This event proved that it is possible to build a non-repeating pattern using only one type of tile (red) and its mirror image (blue) that will repeat infinitely without the pattern of red and blue tiles repeating although an overall pattern of triangles can be seen with the white lines. This was the largest pattern of its kind being built for the first time in the world.
Figure 4: The highlight of the day! Public contributed to the building of a newly discovered form of symmetry. Building this symmetrical pattern involved one type of tile with a certain print (red) and its mirror image (blue). The tiles were designed by Prof. Brian Sutton and Dr Shelley James based on a paper by amateur mathematician Joan Taylor. Using these uniquely designed hexagonal tiles, placement of the tiles followed (two main rules: the white lines had to align and the darker lines had to match orientations) the pattern and positioning of the tiles was certainly unique, and would never be able to repeat itself.
Figure 5: Dr James and Prof. Sutton demonstrating to the audience, with aid of 3D printed glass structures: tartaric acid and racemic acid, the concept of mirror imaging. A group photo of Prof Sutton and Dr James with the team.