http://programmer.ie/tags/gray-scott/ Recent content in Gray Scott on Programmer.ie: Modern AI programming Hugo en-us Mon, 10 Aug 2026 18:42:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-12/ Mon, 10 Aug 2026 18:42:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-12/ <h1 id="cellular-automata-from-first-principles-12-reaction-diffusion-and-pattern-formation">Cellular Automata From First Principles 12: Reaction-Diffusion and Pattern Formation</h1> <p>Diffusion smooths differences.</p> <p>Reaction can amplify them.</p> <p>Put the two processes together and a nearly uniform field can develop persistent spots, stripes and fronts.</p> <p>We will use a discrete Gray-Scott reaction-diffusion simulation because it gives us a compact bridge from local cellular updates to continuous pattern-forming dynamics.</p> <p>Each lattice cell stores two values:</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>U = concentration of chemical U </span></span><span style="display:flex;"><span>V = concentration of chemical V </span></span></code></pre></div><p>So our cell state is now a vector:</p>