The algorithmic beauty of plants
The algorithmic beauty of plants
Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology
On the tiling by translation problem
Discrete Applied Mathematics
Christoffel and Fibonacci tiles
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
An optimal algorithm for detecting pseudo-squares
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Combinatorial properties of double square tiles
Theoretical Computer Science
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It has been proved that, among the polyominoes that tile the plane by translation, the so-called squares tile the plane in at most two distinct ways. In this paper, we focus on double squares, that is, the polyominoes that tile the plane in exactly two distinct ways. Our approach is based on solving equations on words, which allows us to exhibit properties about their shape. Moreover, we describe two infinite families of double squares. The first one is directly linked to Christoffel words and may be interpreted as segments of thick straight lines. The second one stems from the Fibonacci sequence and reveals some fractal features.