Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Communications of the ACM
Programmable self-assembly using biologically-inspired multiagent control
Proceedings of the first international joint conference on Autonomous agents and multiagent systems: part 1
Botanical computing: a developmental approach to generating interconnect topologies on an amorphous computer
Empirical Characterization of Discretization Error in Gradient-Based Algorithms
SASO '08 Proceedings of the 2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems
Local Construction of Near-Optimal Power Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
Integer Gradient for Cellular Automata: Principle and Examples
SASOW '08 Proceedings of the 2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshops
Fast Self-stabilization for Gradients
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
Efficient computation of elliptic gabriel graph
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Fine-grain discrete Voronoi diagram algorithms in L1 and L∞ norms
Mathematical and Computer Modelling: An International Journal
Voronoi-like partition of lattice in cellular automata
Mathematical and Computer Modelling: An International Journal
Convex hulls on cellular automata
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
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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 construct and define metric Gabriel graphs that transport the principles of Gabriel graphs on arbitrary metric space, allowing their use in domains like cellular automata and amorphous computing, or any other domains where a non-Euclidean metric is used. We study global/local properties of metric Gabriel graphs and use them to design a cellular automaton that draws the metric Gabriel graph of its input. This cellular automaton only uses seven states to achieve this goal and has been tested on hexagonal grids, 4-connected, and 8-connected square grids.