CellularAutomata

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A graph containing connected nodes, such that the state of each node in a graph, for the next time slice, is generated by one or more simple constant rules, the same for all nodes, that take into account only the current states of that node and the nodes it is directly connected to.

Most of the best-known CellularAutomata are visualised as taking place on a 2-dimensional square grid.
The state of each cell in the grid, for the next time slice, is generated by one or more simple constant rules, the same for all cells, that take into account only the current states of that cell and its immediately adjacent neighbours. See, for example, ConwaysLife.

Old definition was definitely wrong - I strongly dispute "immediately adjacent" - although I'd have to research an accurate one.

: I'm thinking of "immediately adjacent" as being to do with locality of effect scope, not necessarily position in grid. Usually, the former implies the latter. Certainly all the definitions of CA I've seen say something like "adjacent cells" or "nearest neighbours". How about the revised definition above? - MoonShadow
: All that is required is a map of nodes which are considered connected to each other, or otherwise. Each node has state. The words 'discrete' and 'finite' have their usual meanings as modifiers. The system as a whole evolves using a set of global rules based upon the states of connected nodes. I don't think anything more is required. That such systems are usually drawn upon a minimally connected two dimensional grid is just those are easiest to visualise - I'm pretty sure you're allowed any set of rules to connect your nodes. --Vitenka

      XXXX  
      XXXX 
      XXXX 

            XXXX
            XXXX
            XXXX

XXXX  XXXX  XXXX
XXXX  XXXX  XXXX
XXXX  XXXX  XXXX

In ConwaysLife, for example, the above would turn after one generation into:

        XX 
       X  X  
      X    X 
       X  X 
        XX    XX
             X  X
            X    X
             X  X
  XX    XX
 X  X  X  X  X  X
X    XX    XX    X
 X  X  X  X  X  X
  XX    XX    XX

This is a slightly highbrow joke. The pattern being referred to above is the "glider" from ConwaysLife:

  X
   X
 XXX

It follows this pattern, repeating after four generations (timeslices):

   X
    X    X X     X   X      X
  XXX     XX   X X    XX     X
          X     XX   XX    XXX

Note that the overall pattern has moved down (and right) by one grid step. The "glider" is the simplest "spaceship" (pattern which reproduces itself at a different location) in ConwaysLife.

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