Abstract
In 1704 Father Sébastien Truchet published an article, ‘Mémoire sur les combinaisons’, that describes his mathematical and artistic investigations into how a simple set of square tiles, each divided by a diagonal into a white half and a black half, can be arranged to form an infinity of pleasing designs. In this paper, we describe how to modify Truchet’s tiles so that a collection of them can be used for halftoning, the reproduction of user-supplied greyscale target images in pure black and white. We do this by allowing the diagonals of the tiles to ‘flex’ or bend at their midpoints in accordance with the brightness of an individual pixel, or a collection of pixels, from the target image. We also present hexagonal variations, a similar scheme for the Truchet-like tiles – each decorated with two quarter-circle arcs centred at opposite corners of thesquare – proposed by Cyril Stanley Smith in 1987, and an extension that can be applied to all regular and semiregular tilings.
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