… of an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation
(APF) … However, it is natural to consider the other regular tessellation graphs, that are triangular …

… double periodic graph (A, E) by the Delaunay graph. … a unique solution up to an additive
arbitrary constant vector. … Therefore, a point a on the torus Q 0 is associated to the infinite set of …

… , the Arbitrary Pattern Formation for a set of oblivious asynchronous robots on the infinite …
in which robots move, we consider any regular tessellation graph, that is square, triangular, and …

… In addition, we propose a graph representation that is … developed for CA on regular
tessellations, we present an … , we consider a countably infinite, irregular tessellation 𝒯 of ℝ n . …

… We assume regular tessellation graphs as discretization of the Euclidean plane, and we … ,
the Arbitrary Pattern Formation for a set of oblivious asynchronous robots on the infinite grid in …

… of the arbitrary tessellation into complete, bi-… infinite plane tessellation, the number of
edges scales as N 2 . We define a sub-graph built from the green links only as a “green sub-graph”, …

… graphs beyond square grids, such as triangular and hexagonal grids, and provided an
algorithm that works in any regular tessellation graph. … every robot is active infinitely often. In the …

… A standard way to discretize an arbitrary domain is to use a Voronoi tessellation. On a … Moon,
Pattern formation in a two-dimensional array of oscillators with phase-shifted coupling, Phys…

… In various graph, for example, regular tessellation graphsApf problem was studied in [18]. …
This paper deals with two arbitrary pattern formation problems on an infinite grid. The robots …

… further types of pattern formation phenomena based on the … the thermodynamic limit of
infinite patterns and the transition to … We will admit an arbitrary number of fundamental variables …