We introduce a set of techniques that are used together to produce realistic-looking animations of burning objects. These include a new method for simulating spreading on polygonal meshes. A key component of our approach consists in using individual flames as primitives to animate and render the fire. This simplification enables rapid computation and gives more intuitive control over the simula...

We define a relative version of tiling cohomology for the purpose of comparing the topology of tiling dynamical systems when one is a factor of the other. We illustrate this with examples, and outline a method for computing the cohomology of tiling spaces of finite type.

We introduce the notion of path extensions of tiling semigroups and investigate their properties. We show that the path extension of a tiling semigroup yields a strongly F *-inverse cover of the tiling semigroup and that it is isomorphic to an HNN * extension of its semilattice of idempo-tents.

It is shown that the Socolar tiling, which is quasiperiodic and 12-fold symmetric , can be characterized as the unique tiling which is maximally covered by a suitably pair of clusters. Analogous results can be obtained also for other dodecagonal tilings, among them the shield tiling.

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert’s Nullstellensatz we obtain a necessary condition for tiling n-space by translates of a cluster of cubes. Further, the polynomial method will enable us to show that if there exists a tiling of n-space by translates of a cluster V of prime size then there is a lattice tiling by V as well. Finally, we...

In the framework of perfect loop nests with uniform dependences, tiling is a technique used to group elemental computation points so as to increase computation granularity and to reduce the overhead due to communication time. We review existing approaches from the literature, together with the optimization criteria that are used for determining a \good" or \optimal" tiling. Then we explain the ...

We have recently shown that p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite self-assembles into a two-dimensional rhombus random tiling. This tiling is close to ideal, displaying long-range correlations punctuated by sparse localized tiling defects. In this article we explore the analogy between dynamic arrest in this type of random tilings and that of structural glasses. We sho...

This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the “tiles” have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods. A thorough examination of spotlight tilings o...

In this paper, we give a combinatorial formalization that describes a wide range of related problems in the theory of tiling derived from the popular game of dominos. We show that determining if a given finite region of the plane can be tiled with a given set of dominos is NP-Complete. The new graph theoretical methods we introduce allow this result to be easily generalized to a variety of simi...

Abstract. This article introduces spotlight tiling, a type of covering for a region which is similar to tiling. The distinguishing aspects of spotlight tiling are that the “tiles” have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods. A thorough examination...