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    <title>Elementary Cellular Automata on Programmer.ie: Modern AI programming</title>
    <link>http://programmer.ie/tags/elementary-cellular-automata/</link>
    <description>Recent content in Elementary Cellular Automata on Programmer.ie: Modern AI programming</description>
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    <lastBuildDate>Tue, 11 Aug 2026 01:08:00 +0100</lastBuildDate>
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      <title>Digital Life 02: Remove Almost Everything</title>
      <link>http://programmer.ie/books/digital-life/02-remove-almost-everything/</link>
      <pubDate>Tue, 11 Aug 2026 01:08:00 +0100</pubDate>
      <guid>http://programmer.ie/books/digital-life/02-remove-almost-everything/</guid>
      <description>&lt;p&gt;In the previous chapter we started with something complicated.&lt;/p&gt;&#xA;&lt;p&gt;A continuous field.&lt;/p&gt;&#xA;&lt;p&gt;A smooth neighborhood.&lt;/p&gt;&#xA;&lt;p&gt;A growth process.&lt;/p&gt;&#xA;&lt;p&gt;Localized structures that moved through space.&lt;/p&gt;&#xA;&lt;p&gt;Patterns that looked disturbingly creature-like.&lt;/p&gt;&#xA;&lt;p&gt;That was useful because it gave us a mystery.&lt;/p&gt;&#xA;&lt;p&gt;Now we are going to destroy almost all of it.&lt;/p&gt;&#xA;&lt;p&gt;Not gradually.&lt;/p&gt;&#xA;&lt;p&gt;Aggressively.&lt;/p&gt;&#xA;&lt;p&gt;We want to know:&lt;/p&gt;&#xA;&lt;blockquote&gt;&#xA;&lt;p&gt;&lt;strong&gt;How little machinery can remain before interesting organization disappears?&lt;/strong&gt;&lt;/p&gt;&lt;/blockquote&gt;&#xA;&lt;p&gt;Start with the kind of system we saw in Lenia.&lt;/p&gt;</description>
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      <title>Cellular Automata From First Principles 23: Search All 256 Elementary Rules</title>
      <link>http://programmer.ie/post/cellular-automata-from-first-principles-23/</link>
      <pubDate>Mon, 10 Aug 2026 18:56:00 +0100</pubDate>
      <guid>http://programmer.ie/post/cellular-automata-from-first-principles-23/</guid>
      <description>&lt;h1 id=&#34;cellular-automata-from-first-principles-23-search-all-256-elementary-rules&#34;&gt;Cellular Automata From First Principles 23: Search All 256 Elementary Rules&lt;/h1&gt;&#xA;&lt;p&gt;Elementary cellular automata give us a rare luxury.&lt;/p&gt;&#xA;&lt;p&gt;The complete rule space is tiny.&lt;/p&gt;&#xA;&lt;p&gt;There are only:&lt;/p&gt;&#xA;&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; style=&#34;color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;&#34;&gt;&lt;code class=&#34;language-text&#34; data-lang=&#34;text&#34;&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;256 rules&#xA;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;So we do not need sampling, intuition or famous examples.&lt;/p&gt;&#xA;&lt;p&gt;We can evaluate every rule.&lt;/p&gt;&#xA;&lt;hr&gt;&#xA;&lt;h2 id=&#34;build-an-experiment-runner&#34;&gt;Build an experiment runner&lt;/h2&gt;&#xA;&lt;p&gt;Assume we already have:&lt;/p&gt;&#xA;&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; style=&#34;color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;&#34;&gt;&lt;code class=&#34;language-python&#34; data-lang=&#34;python&#34;&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;run_rule(rule_number, width, generations, initial_state)&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;fingerprint(history)&#xA;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;Then exhaustive search is simple:&lt;/p&gt;&#xA;&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; style=&#34;color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;&#34;&gt;&lt;code class=&#34;language-python&#34; data-lang=&#34;python&#34;&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;&lt;span style=&#34;color:#66d9ef&#34;&gt;def&lt;/span&gt; &lt;span style=&#34;color:#a6e22e&#34;&gt;scan_rules&lt;/span&gt;(initial_state, width&lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt;&lt;span style=&#34;color:#ae81ff&#34;&gt;201&lt;/span&gt;, generations&lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt;&lt;span style=&#34;color:#ae81ff&#34;&gt;200&lt;/span&gt;):&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;    records &lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt; []&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;    &lt;span style=&#34;color:#66d9ef&#34;&gt;for&lt;/span&gt; rule &lt;span style=&#34;color:#f92672&#34;&gt;in&lt;/span&gt; range(&lt;span style=&#34;color:#ae81ff&#34;&gt;256&lt;/span&gt;):&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;        history &lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt; run_rule(&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;            rule,&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;            width&lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt;width,&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;            generations&lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt;generations,&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;            initial_state&lt;span style=&#34;color:#f92672&#34;&gt;=&lt;/span&gt;initial_state,&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;        )&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;        records&lt;span style=&#34;color:#f92672&#34;&gt;.&lt;/span&gt;append({&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;            &lt;span style=&#34;color:#e6db74&#34;&gt;&amp;#34;rule&amp;#34;&lt;/span&gt;: rule,&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;            &lt;span style=&#34;color:#f92672&#34;&gt;**&lt;/span&gt;fingerprint(history),&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;        })&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;    &lt;span style=&#34;color:#66d9ef&#34;&gt;return&lt;/span&gt; records&#xA;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;The hard part is no longer execution.&lt;/p&gt;</description>
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