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—When programming a spatial computing medium such as a cellular automaton, the hop count distance to some set of sources (particles) is an often used information. In particular, we consider the case where the sources themselves are moving. Due to the locality of communication, only an estimation of the distance can be made at each time step, and each… (More)

Gabriel graphs are subgraphs of Delaunay graphs that are used in many domains such as sensor networks and computer graphics. Although very useful in their original form, their definition is bounded to applications involving Euclidean spaces only, but their principles seem to be applicable to a wider range of applications. In this article, we generalize this… (More)

In this paper, we consider Global Graph Transformations where all occurrences of a set of predefined local rules are applied altogether synchronously so that each part of the original graph gives rise to a part of the result graph, without any reference to the original one. The particularity here is that our framework is deterministic. This is achieved by… (More)

—In the cellular automata domain, the discrete convex hull computation rules proposed until now only deal with a connected set of seeds in infinite space, or with distant set of seeds in finite space. Taking a spatial computing point of view, we present a cellular automata rule that constructs the discrete convex hull of arbitrary set of seeds in infinite… (More)