# Robert Bosch

The mathematician in me is fascinated with the various roles that constraints play in optimization problems: sometimes they make problems much harder to solve; other times, much easier. And the artist in me is fascinated with the roles that constraints play in art. All artists must deal with constraints, and many artists choose to impose constraints upon themselves. The benefit of this was well expressed by Joseph Heller (paraphrasing T.S. Eliot): 'If one is forced to write within a certain framework, the imagination is taxed to its utmost and will produce its richest ideas.'

Father Sébastien Truchet (1657-1729) was a Carmelite clergyman. He was King Louis XIV's favorite hydraulic engineer. He designed fonts. And in 1704 he published an article, "Mémoire sur les combinaisons," that described 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 patterns. Today, Truchet's tiles are known as, well, Truchet tiles. To create a Truchet-tile portrait of Truchet, I started with the orientations specified by Pattern D of Plate 1 of Truchet's article. I then allowed the diagonals of the tiles to "flex" or bend at their midpoints. To make a tile darker, I would flex the diagonal into the black half. To make a tile brighter, I would flex the diagonal into the white half. With my Flexible Truchet Tiles, I can approximate any grayscale image, using the image to "warp" any initial pattern of Truchet tiles.