http://programmer.ie/tags/rule-184/ Recent content in Rule 184 on Programmer.ie: Modern AI programming Hugo en-us Mon, 10 Aug 2026 18:38:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-10/ Mon, 10 Aug 2026 18:38:00 +0100 http://programmer.ie/post/cellular-automata-from-first-principles-10/ <h1 id="cellular-automata-from-first-principles-10-simulate-traffic-with-rule-184">Cellular Automata From First Principles 10: Simulate Traffic with Rule 184</h1> <p>Rule 184 is a beautiful example of moving from an abstract rule table to a model with a concrete interpretation.</p> <p>Use a one-dimensional ring road:</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>1 = car </span></span><span style="display:flex;"><span>0 = empty road </span></span></code></pre></div><p>A car moves one cell to the right when the destination is empty.</p> <p>That is enough to produce free flow, queues and a macroscopic density-flow relationship.</p> <hr> <h2 id="write-the-traffic-mechanism-directly">Write the traffic mechanism directly</h2> <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:#f92672">import</span> numpy <span style="color:#66d9ef">as</span> np </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">def</span> <span style="color:#a6e22e">traffic_step</span>(road): </span></span><span style="display:flex;"><span> cars <span style="color:#f92672">=</span> road <span style="color:#f92672">==</span> <span style="color:#ae81ff">1</span> </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> empty_ahead <span style="color:#f92672">=</span> ( </span></span><span style="display:flex;"><span> np<span style="color:#f92672">.</span>roll(road, <span style="color:#f92672">-</span><span style="color:#ae81ff">1</span>) <span style="color:#f92672">==</span> <span style="color:#ae81ff">0</span> </span></span><span style="display:flex;"><span> ) </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> moving <span style="color:#f92672">=</span> cars <span style="color:#f92672">&amp;</span> empty_ahead </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> next_road <span style="color:#f92672">=</span> road<span style="color:#f92672">.</span>copy() </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> next_road[moving] <span style="color:#f92672">=</span> <span style="color:#ae81ff">0</span> </span></span><span style="display:flex;"><span> next_road[ </span></span><span style="display:flex;"><span> np<span style="color:#f92672">.</span>roll(moving, <span style="color:#ae81ff">1</span>) </span></span><span style="display:flex;"><span> ] <span style="color:#f92672">=</span> <span style="color:#ae81ff">1</span> </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">return</span> next_road </span></span></code></pre></div><p>The road is periodic, so the final road cell connects back to the first.</p>