In the simplest models, a cell can be identified by only an integer, indicating either the phase in phase transformation problems or grain id for grain growth o

In the simplest models, a cell can be identified by only an integer, indicating either the phase in phase transformation problems or grain id for grain growth or recrystallization. But, in the more complex models, a cell can include all kind of properties (chemical composition, crystallographic orientation, dislocation density...). The number of neighbors we use also varies. Sometimes, even inside the same CA model, we use a different number of neighbors to calculate the evolution of different properties. Some problems are more related with the boundary between cells, and there we have to use first order, but other properties depend on the bulk and we use second order neighbors too (of course, weighted accordingly). Electron microscopy results are commonly obtained in hexagonal grids, so hexagonal grids are often used in 2D simulations. If you are interested in the topic, you can see for example http://www.dierk-raabe.com/reprints/cellular-automata/ http://www.dierk-raabe.com/reprints/cellular-automata/