The Flat Tile Set Enables Non-midpoint Tile Edge Crossings
Lars Eriksson

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 147–154
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Abstract

This paper focuses on pattern creation, specifically using a technique that incorporates modular tiles within 5-fold patterns. These tiles feature a motif that crosses over each side, interacting with the motif on the adjacent tiles. The novelty of this paper lies in the introduction of crossings that are not at midpoint. Previous papers focused on non- equilateral tiles, but all tiles had midpoint crossings. Here I introduce the first non-midpoint tile set, called the Flat tile set, by presenting the core tile of the set, called the Fone tile. The Flat tile set is the missing link between two types of historical patterns, the Starry and the Floral pattern types (terms coined by Castera). When the two types are found together in existing traditional Islamic geometric patterns, one is often more dominant over the other and the other is concentrated around star formations. As Flat tiles link these two worlds together, they enable a wider spectrum of historical patterns to be tiled and gives promise to new interesting patterns. Now, both types can grow and claim equal part of the pattern.

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