http://programmer.ie/tags/rule-space/ Recent content in Rule Space on Programmer.ie: Modern AI programming Hugo en-us Mon, 10 Aug 2026 18:57:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-24/ Mon, 10 Aug 2026 18:57:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-24/ <h1 id="cellular-automata-from-first-principles-24-search-larger-rule-spaces">Cellular Automata From First Principles 24: Search Larger Rule Spaces</h1> <p>The 256 elementary rules are small enough to enumerate.</p> <p>Most interesting cellular-automata design spaces are not.</p> <p>Add more states, a larger neighborhood, continuous parameters, or several channels and exhaustive search quickly becomes impossible.</p> <p>So we need search strategies.</p> <hr> <h2 id="why-the-rule-space-explodes">Why the rule space explodes</h2> <p>For <code>k</code> possible cell states and a neighborhood containing <code>n</code> cells, there are:</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>k^n possible neighborhood configurations </span></span></code></pre></div><p>A deterministic rule chooses one of <code>k</code> outputs for every configuration, giving:</p>