Mirrored Image Montages
Vincent Schumacher

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 475–478
Short Papers

Abstract

This paper describes a technique for filling a plane with geometric tiles that have no gaps or overlaps; an important feature of these tiles is that each one has an image on it, and the tiles must be connected seamlessly. That is, for each pair of adjacent tiles, the edge between them is a line of symmetry for the image formed by those two tiles. To make such an image, multiple copies of a single tile and its reflection can be connected. The artistic purpose of this technique is to ensure that the tiles will form a whole image with no obvious visual breaks between tiles. The mathematical result is that when tiles are connected seamlessly, they may or may not correspond to tessellations, and some tessellations cannot be used as a template for a seamless image.

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