http://programmer.ie/tags/dynamics/ Recent content in Dynamics on Programmer.ie: Modern AI programming Hugo en-us Mon, 10 Aug 2026 18:51:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-18/ Mon, 10 Aug 2026 18:51:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-18/ <h1 id="cellular-automata-from-first-principles-18-activity-density-and-change">Cellular Automata From First Principles 18: Activity, Density and Change</h1> <p>A cellular automaton can look busy while doing very little that persists.</p> <p>It can also look visually quiet while preserving a small moving structure for hundreds of generations.</p> <p>So we need to separate several properties that are easy to confuse:</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-text" data-lang="text"><span style="display:flex;"><span>occupancy </span></span><span style="display:flex;"><span>temporal change </span></span><span style="display:flex;"><span>spatial variation </span></span><span style="display:flex;"><span>persistence </span></span></code></pre></div><p>This chapter turns those ideas into explicit measurements.</p> <p>Together they form our first useful <strong>behavioral fingerprint</strong>.</p>