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<html><head>
<title>Fractal Geometry Summer Workshop</title></head>
<body bgcolor="WHITE">
<h1 align="center">4. C. Examples of Cellular Automata Patterns</h1>


<p align="justify">First, an example.  Recall from an initial generation with a
single live cell the N = 3, S = 2 rule produces the pattern

<table>
<tbody><tr><td><img src="CAPatterns_files/CARule1.gif" width="340" height="60">
</td><td><img src="CAPatterns_files/CAPattern1.gif" width="217" height="102">
</td></tr></tbody></table>

</p><p align="justify">This rule produces the pattern, easy to guess

<table>
<tbody><tr><td><img src="CAPatterns_files/CARule2.gif" width="340" height="60">
</td><td><img src="CAPatterns_files/CAPattern2.gif" width="217" height="102">
</td></tr></tbody></table>

</p><p align="justify">

<table>
<tbody><tr><td>So the rule here should produce two lines, one going right, one
going left, right?  That is the most frequent quess.  Is it correct?  Think a
moment, then look at the <a href="http://classes.yale.edu/99-00/math190a/CAPattern3.gif">answer</a>.
</td><td><img src="CAPatterns_files/CARule3.gif" width="340" height="60">
</td></tr></tbody></table>

</p><p align="justify">A few more <a href="http://classes.yale.edu/99-00/math190a/CAPExamples.html">examples</a> illustrate
the richness of the behavior of one-dimensional binary N = 3 CA.


</p><p align="justify">Changing the rules obviously can have a large influence on the
pattern that evolved.  For some automata there is another type of sensitivity:
changing the <a href="http://classes.yale.edu/99-00/math190a/CASensitivity.html">initial conditions</a> can have a large effect.


</p><p align="justify">Not surprisingly, <a href="http://classes.yale.edu/99-00/math190a/2DCAExamples.html">two-dimensional</a>
CA also exhibit a rich variety of
patterns.  We cannot easily view the spacetime patterns of these.  Rather, we present
pictures of a single generation.

</p><p align="justify">The best-known of all CA is John Conway's
<a href="http://classes.yale.edu/99-00/math190a/Life.html">game of life</a>.

</p><p align="justify">With the remarkable range of behavior demonstrated by CA, a
natural question is can the behaviors be <a href="http://classes.yale.edu/99-00/math190a/Wolfram.html">classified</a>?
If so, are there calculations to <a href="http://classes.yale.edu/99-00/math190a/Langton.html">predict</a> the behavior?

</p><p align="justify">Continue to <a href="http://classes.yale.edu/99-00/math190a/GA.html">
4. D. Genetic Algorithms and Artificial Evolution</a>

</p><p align="justify">Return to <a href="http://classes.yale.edu/99-00/math190a/CABasics.html">4. B. Cellular Automata Basics</a>

</p><p align="justify">Return to <a href="http://classes.yale.edu/99-00/math190a/welcomeCA.html">4. Cellular Automata and Fractal Evolution</a>

</p><p align="justify">

</p></body></html>