About 300 years ago Sébastien Truchet systematically studied patterns that could be formed from square tiles that were divided by a diagonal into a white triangle and a black triangle. Other pattern creators have been inspired by him to make Truchet-like tilings composed of circular arcs and other motifs. These tilings are all based on Euclidean tessellations, usually the tiling by squares. In ...

1. Rep-tiling. This paper provides a short survey of recent work by the author on self-replicating tilings, a subject that has recently come under independent investigation by several mathematicians, for example Grr ochenig and Hass 11], Grr ochenig and Madyeh 10], Kenyon 14], Kitto, Vince and Wilson 15] and Vince 21] 22]. These tilings have application to computer addressing 5] 15] 20] and to ...

Tiling is a key transformation used for coarsening the granularity of parallelism and improving locality. It is known that current stateof-the-art compiler approaches for tiling affine loop nests make use of sufficient, i.e., conservative conditions for the validity of tiling. These conservative conditions, which are used for static scheduling, miss tiling schemes for which the tile schedule is...

Storage management of multidimensional arrays aims at supporting the array model needed by applications and insuring fast execution of access operations. Current approaches to store multidimensional arrays rely on partitioning data into chunks (equally sized subarrays). Regular partitioning, however, does not adapt to access patterns, leading to suboptimal access performance. In this paper, we ...

Responding to Kwaśniewski’s cobweb posets’ problems posed in [3, 4] we present here some results on one of them namely on Cobweb Tiling Problem. Kwaśniewski cobweb posets with tiling property are designated-coded by their correspondent tiling sequences. We show that the family of all cobweb tiling sequences includes Natural numbers, Fibonacci numbers, Gaussian integers and show that there are m...