Discrete Parabolas and Circles on 2D Cellular Automata

,andpossiblythehexagonalnetwork. Wecallcell each pair {vertex,automaton A}.Such a system can be considered as a dynamical one. At one time t,the global state of the system is given by an application Γ −→ S,whichassigns to each cell a state of A.And,startingfromaninitialconfiguration,the whole system synchronously evolves, at discrete times, from one config-uration to the next one. This behavior is formalized through asequenceofconfigurations (Γ