http://programmer.ie/tags/complexity/ Recent content in Complexity on Programmer.ie: Modern AI programming Hugo en-us Tue, 11 Aug 2026 01:19:00 +0100 http://programmer.ie/books/digital-life/03-the-first-surprise/ Tue, 11 Aug 2026 01:19:00 +0100 http://programmer.ie/books/digital-life/03-the-first-surprise/ <p>We ended the last chapter by changing one number.</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>rule <span style="color:#f92672">=</span> <span style="color:#ae81ff">22</span> </span></span></code></pre></div><p>became:</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>rule <span style="color:#f92672">=</span> <span style="color:#ae81ff">30</span> </span></span></code></pre></div><p>Nothing else changed.</p> <p>Same world.</p> <p>Same single active cell.</p> <p>Same three-cell neighborhood.</p> <p>Same synchronous update.</p> <p>Same periodic boundary.</p> <p>Same eight-bit lookup mechanism.</p> <p>Only the rule changed.</p> <p>And the spacetime diagram stopped looking simple.</p> <p><img src="http://programmer.ie/images/books/digital-life/ch03-rule30-hero.png" alt="Rule 30 from a single active cell"></p> <p>There is visible structure on the left.</p> <p>There is irregularity on the right.</p> <p>There are repeating fragments.</p> <p>There are regions that look almost patterned and then break apart.</p>