title: Stablized cellular automation
body: <p>I'm working on cellular automation simulation.
  Rule are the following:</p>
  <ul>
  <li>Each cell interacts with its Moore's neighborhood to update its value.</li>
  <li>The cell is in any infinite-dimensional grid.</li>
  <li>The cell may have a randomized initial value.</li>
  <li>Rules are stable, after a certain iteration, they will converge to a uniform state.</li>
  </ul>
  <p>It's not necessary for a certain programming language so we only have basic datatypes i.e. bool, int, their's n-dimensional array, etc. in this algorithm.</p>
  <p>I have an initial value of any cell that I can load into the memory whenever I wanted. Is there any algorithm to calculate its stabilized value without looping the whole infinite grid?</p>
  <p>To be specific, what I'm working on is a rule B5678/S45678 2 dimensional life-like cellular automation.</p>