http://programmer.ie/tags/cycles/ Recent content in Cycles on Programmer.ie: Modern AI programming Hugo en-us Mon, 10 Aug 2026 18:53:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-20/ Mon, 10 Aug 2026 18:53:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-20/ <h1 id="cellular-automata-from-first-principles-20-periodicity-and-attractors">Cellular Automata From First Principles 20: Periodicity and Attractors</h1> <p>Many cellular automata eventually repeat.</p> <p>A fixed point repeats every generation.</p> <p>An oscillator repeats after several generations.</p> <p>On a finite grid, deterministic cellular automata must eventually revisit a previous state because only finitely many states exist.</p> <p>That makes cycle detection a fundamental measurement.</p> <hr> <h2 id="hash-each-state">Hash each state</h2> <p>For binary arrays we can store the bytes:</p> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-python" data-lang="python"><span style="display:flex;"><span><span style="color:#66d9ef">def</span> <span style="color:#a6e22e">state_key</span>(state): </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">return</span> state<span style="color:#f92672">.</span>tobytes() </span></span></code></pre></div><p>Then track when each state first appeared:</p>