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	<title>Comments on: Longevity in Conway&#039;s Game of Life Revisited</title>
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	<link>http://www.nathanieljohnston.com/2009/07/longevity-in-conways-game-of-life-revisited/</link>
	<description>A blog of recreational math and quantum information theory</description>
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		<title>By: Nathaniel Johnston &#187; The Maximal Lifespan of Patterns in Conway&#8217;s Game of Life</title>
		<link>http://www.nathanieljohnston.com/2009/07/longevity-in-conways-game-of-life-revisited/#comment-97</link>
		<dc:creator>Nathaniel Johnston &#187; The Maximal Lifespan of Patterns in Conway&#8217;s Game of Life</dc:creator>
		<pubDate>Fri, 31 Jul 2009 13:58:39 +0000</pubDate>
		<guid isPermaLink="false">http://www.nathanieljohnston.com/?p=493#comment-97</guid>
		<description>[...] a couple of recent posts, I argued that random patterns in Conway&#8217;s Game of Life tend, on average, to live longest [...]</description>
		<content:encoded><![CDATA[<p>[...] a couple of recent posts, I argued that random patterns in Conway&#8217;s Game of Life tend, on average, to live longest [...]</p>
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		<title>By: Nathaniel</title>
		<link>http://www.nathanieljohnston.com/2009/07/longevity-in-conways-game-of-life-revisited/#comment-96</link>
		<dc:creator>Nathaniel</dc:creator>
		<pubDate>Mon, 20 Jul 2009 15:42:43 +0000</pubDate>
		<guid isPermaLink="false">http://www.nathanieljohnston.com/?p=493#comment-96</guid>
		<description>&lt;a href=&quot;#comment-617&quot; rel=&quot;nofollow&quot;&gt;@Macbi&lt;/a&gt; - You&#039;re quite right -- there was a bug in the script! I have updated the script so that it is bug-free now, but here&#039;s what the problem was:

The script checks for stability by storing hashes of each generation and checks for hash collisions. When a hash collision is found, it marks the pattern as stable and records the generation number of the generation that it collided with. Unfortunately, the script was not properly clearing out the hash list after each new pattern was generated (this is what is fixed now). Thus, if a pattern ever stabilized with an empty field in generation 2 at 98%, that generation 2 would also get marked down for 99%, even though it almost surely stabilized at generation 1.

The good news is that this problem would only ever come up if two consecutive patterns stabilized to the exact same pattern, which almost always would be the empty field, meaning the middle densities (i.e., the interesting ones) were unaffected by the bug. I ran the bug-free script for 1000 trials just to make sure that the resulting graphs look pretty much the same as the ones included with this post, and they do.

Good catch!</description>
		<content:encoded><![CDATA[<p><a href="#comment-617" rel="nofollow">@Macbi</a> &#8211; You&#8217;re quite right &#8212; there was a bug in the script! I have updated the script so that it is bug-free now, but here&#8217;s what the problem was:</p>
<p>The script checks for stability by storing hashes of each generation and checks for hash collisions. When a hash collision is found, it marks the pattern as stable and records the generation number of the generation that it collided with. Unfortunately, the script was not properly clearing out the hash list after each new pattern was generated (this is what is fixed now). Thus, if a pattern ever stabilized with an empty field in generation 2 at 98%, that generation 2 would also get marked down for 99%, even though it almost surely stabilized at generation 1.</p>
<p>The good news is that this problem would only ever come up if two consecutive patterns stabilized to the exact same pattern, which almost always would be the empty field, meaning the middle densities (i.e., the interesting ones) were unaffected by the bug. I ran the bug-free script for 1000 trials just to make sure that the resulting graphs look pretty much the same as the ones included with this post, and they do.</p>
<p>Good catch!</p>
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		<title>By: Nathaniel Johnston &#187; Longest-Lived Soup Density in Conway&#8217;s Game of Life</title>
		<link>http://www.nathanieljohnston.com/2009/07/longevity-in-conways-game-of-life-revisited/#comment-95</link>
		<dc:creator>Nathaniel Johnston &#187; Longest-Lived Soup Density in Conway&#8217;s Game of Life</dc:creator>
		<pubDate>Mon, 20 Jul 2009 02:58:52 +0000</pubDate>
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		<description>[...] [July 19, 2009]: See this post, which deals with soup longevity on a [...]</description>
		<content:encoded><![CDATA[<p>[...] [July 19, 2009]: See this post, which deals with soup longevity on a [...]</p>
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		<title>By: Macbi</title>
		<link>http://www.nathanieljohnston.com/2009/07/longevity-in-conways-game-of-life-revisited/#comment-94</link>
		<dc:creator>Macbi</dc:creator>
		<pubDate>Fri, 17 Jul 2009 19:39:42 +0000</pubDate>
		<guid isPermaLink="false">http://www.nathanieljohnston.com/?p=493#comment-94</guid>
		<description>Speaking of statistical anomalies, I&#039;ve noticed that in the raw data you supply, when a 99% density trial has a life span of 2, the 98% trial with the same trial number also does. I haven&#039;t had a chance to look at the script, but it happens far to consistently to be chance.</description>
		<content:encoded><![CDATA[<p>Speaking of statistical anomalies, I&#8217;ve noticed that in the raw data you supply, when a 99% density trial has a life span of 2, the 98% trial with the same trial number also does. I haven&#8217;t had a chance to look at the script, but it happens far to consistently to be chance.</p>
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