Critical connectivity in cellular automata

This series of images illustrates the effect of connectivity on invasion percolation in a cellular automaton . Suppose that the cellular automaton represents an epidemic (for example, spread of a disease) or flow through a medium (for example, water seeping through porous rock). Then the ‘active’ sites might represent susceptible plants in a field, or cavities in a rock.

aboutlogo.gif

If the number of active cells is:

  • sub-critical (here 55%), the process halts almost immediately.
  • super-critical (here 65%), the process absorbs almost all of the active cells.
  • critical (here ~60%), the process typically spreads, but leaves large areas untouched. The variance in size of the affected area is also maximum at the critical level, as also is the time required for the process to run to completion.

This phenomenon is a consequence of changing connectivity patterns. For further discussion of this phenomenon, and its biological implications, see the paper Emergent behaviour in biological systems.