We consider two formulations of a cellular automata: the first one uses a gather-update paradigm and the second one a collision-propagation paradigm. We show the equivalence of both descriptions and, using the latter paradigm, we propose a simple way to define a Cellular Automata on a graph with arbitrary topology. Finally, we exploit the duality of formulation to reconsider the problem of characterizing invertible cellular automata.
['Bastien Chopard', 'Jean-Luc Falcone', 'Ranaivo Mahaleo Razakanirina', 'Alfons G. Hoekstra', 'Alfonso Caiazzo']
On the Collision-Propagation and Gather-Update Formulations of a Cellular Automata Rule